Talk:Greatest prime dividing the n-th cubefree number: Difference between revisions

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(→‎The logic of cubes_before(): analog to Totient function?)
(→‎The logic of cubes_before(): legendre Prime countiing)
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== The logic of cubes_before() ==
== The logic of cubes_before() ==
Fairly obviously there are 31 multiples of 8(2^3) less than 249, and 9 multiples of 27(3^3), however of course we have to account for 8*27 = 216 being in both. I'm pretty sure it's fairly standard fare, but the logic of accounting for >=3 such clashes is eluding me. --[[User:Petelomax|Petelomax]] ([[User talk:Petelomax|talk]]) 02:07, 6 March 2024 (UTC)
Fairly obviously there are 31 multiples of 8(2^3) less than 249, and 9 multiples of 27(3^3), however of course we have to account for 8*27 = 216 being in both. I'm pretty sure it's fairly standard fare, but the logic of accounting for >=3 such clashes is eluding me. --[[User:Petelomax|Petelomax]] ([[User talk:Petelomax|talk]]) 02:07, 6 March 2024 (UTC)
:Would something like a modified "Totient function" something adequate.<br>'''counts the integers up to a given positive integer n that are relatively prime to n'''<br>[[Totient_function#C]]<br>Instead testing with primes than only with primes cubed.Needed to be tested. --[[User:Horst|Horst]] ([[User talk:Horst|talk]]) 19:20, 6 March 2024 (UTC)
:Would something like a modified [[Legendre_prime_counting_function]] something adequate.<br>Instead testing with primes than only with primes cubed.[[Legendre_prime_counting_function#Non-recursive_partial_sieve]] --[[User:Horst|Horst]] ([[User talk:Horst|talk]]) 04:09, 7 March 2024 (UTC)