Problem 53009. Easy Sequences 48: Prime Big Omega of Factorial Sequence

Created by Ramon Villamangca

Solve Later

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<div style = "text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 272px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">For an integer </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">n</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">, the </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Prime_omega_function"><span style=""><span style="">prime big omega</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""> function, </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="33.5" height="19" style="width: 33.5px; height: 19px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">, is defined as the total number of prime factors of </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">n</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">. So, if  </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="51.5" height="18" style="width: 51.5px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">, since </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="103.5" height="19" style="width: 103.5px; height: 19px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">, therefore </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="149.5" height="19" style="width: 149.5px; height: 19px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; ">Given an integer </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">n</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; ">, write a function that evaluates the following summation:</span></span></div><div style="block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">            </span></span><span style="vertical-align:-17px"><img src="data:image/png;base64,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" width="59" height="46" style="width: 59px; height: 46px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; "> </span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">For example for </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="36.5" height="18" style="width: 36.5px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">:</span></span></div><div style="block-size: 76px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">            </span></span><span style="vertical-align:-32px"><img 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" width="525.5" height="76" style="width: 525.5px; height: 76px;"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">In this case therefore, the function should return </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="18" height="18" style="width: 18px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">.</span></span></div></div></div>

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Last Solution submitted on Jan 08, 2023

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Solution 6847299

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3 Comments

Ramon Villamangca on 8 Nov 2021

Hi William,

I can't figure out why we are getting different "end digits" for test #9, n = 80000000 to 150000000. Although we basically have same logic. The only difference is my inner loop is vectorized instead of a 'while' loop.

I hope other players could settle this. Might be a rounding issue.

William on 8 Nov 2021

Hi Ramon,

The problem seems to be overflow of some of the intermediate values in the calculation. I put in a test for this, and it fixed all the values in test #9 except the first.

Ramon Villamangca on 9 Nov 2021

HI William,

You're right test #9 is exceeding 'flintmax'. I've removed that test and modified test #8 to prevent lookups. Thanks.

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Problem 53009. Easy Sequences 48: Prime Big Omega of Factorial Sequence

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Problem 53009. Easy Sequences 48: Prime Big Omega of Factorial Sequence

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