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

1,1

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A139574, A175751.

Sequence in context: A348627 A216682 A348521 * A179746 A096472 A306492

Adjacent sequences: A175749 A175750 A175751 * A175753 A175754 A175755

Keyword

nonn

Author

Jaroslav Krizek, Aug 27 2010

Status

approved