cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A175752 Numbers with 45 divisors.

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%I A175752 #22 May 05 2023 10:11:21
%S A175752 3600,7056,8100,15876,17424,19600,20736,22500,24336,39204,41616,48400,
%T A175752 51984,54756,67600,76176,86436,93636,94864,99225,104976,115600,116964,
%U A175752 121104,122500,132496,138384,144400,147456,160000,171396,197136
%N A175752 Numbers with 45 divisors.
%C A175752 Numbers of the forms p^44, p^14*q^2, p^8*q^4 (squares of A189988) and p^4*q^2*r^2 (A179746), where p, q, and r are distinct primes.
%H A175752 T. D. Noe, <a href="/A175752/b175752.txt">Table of n, a(n) for n = 1..1000</a>
%H A175752 OEIS Wiki, <a href="https://oeis.org/wiki/Index_entries_for_number_of_divisors">Index entries for number of divisors</a>
%F A175752 A000005(a(n)) = 45.
%F A175752 Sum_{n>=1} 1/a(n) = (P(2)^2*P(4) - P(4)^2)/2 - P(2)*P(6) + P(8) + P(2)*P(14) - P(16) + P(4)*P(8) - P(12) + P(44) = 0.00133023..., where P is the prime zeta function. - _Amiram Eldar_, Jul 03 2022
%t A175752 Select[Range[400000],DivisorSigma[0,#]==45&] (* _Vladimir Joseph Stephan Orlovsky_, May 06 2011 *)
%o A175752 (PARI) is(n)=numdiv(n)==45 \\ _Charles R Greathouse IV_, Jun 19 2016
%Y A175752 Cf. A000005, A139574, A175751.
%K A175752 nonn
%O A175752 1,1
%A A175752 _Jaroslav Krizek_, Aug 27 2010