A175752 Numbers with 45 divisors.

3600, 7056, 8100, 15876, 17424, 19600, 20736, 22500, 24336, 39204, 41616, 48400, 51984, 54756, 67600, 76176, 86436, 93636, 94864, 99225, 104976, 115600, 116964, 121104, 122500, 132496, 138384, 144400, 147456, 160000, 171396, 197136

Offset: 1

Author

Jaroslav Krizek, Aug 27 2010

Keywords

• nonn

Comments

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.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• OEIS Wiki, Index entries for number of divisors

Crossrefs

Cf. A000005, A139574, A175751.

Programs

Mathematica

Select[Range[400000],DivisorSigma[0,#]==45&] (* Vladimir Joseph Stephan Orlovsky, May 06 2011 *)

PARI

is(n)=numdiv(n)==45 \\ Charles R Greathouse IV, Jun 19 2016

Formula

A000005(a(n)) = 45.

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