A137488 Numbers with 25 divisors.

1296, 10000, 38416, 50625, 194481, 234256, 456976, 1185921, 1336336, 1500625, 2085136, 2313441, 4477456, 6765201, 9150625, 10556001, 11316496, 14776336, 16777216, 17850625, 22667121, 29986576, 35153041, 45212176, 52200625

Offset

1,1

Comments

Maple implementation: see A030513.

Numbers of the form p^24 (24th powers of A000040, subset of A010812) or p^4*q^4 (A189991), where p and q are distinct primes. - R. J. Mathar, Mar 01 2010

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Formula

A000005(a(n)) = 25.

Sum_{n>=1} 1/a(n) = (P(4)^2 - P(8))/2 + P(24) = 0.000933328..., where P is the prime zeta function. - Amiram Eldar, Jul 03 2022

Mathematica

lst = {}; Do[If[DivisorSigma[0, n] == 25, Print[n]; AppendTo[lst, n]], {n, 55000000}]; lst (* Vladimir Joseph Stephan Orlovsky, May 03 2011 *)
Select[Range[5221*10^4], DivisorSigma[0, #]==25&] (* Harvey P. Dale, Mar 11 2019 *)

Prog

(Haskell)
a137488 n = a137488_list !! (n-1)
a137488_list = m (map (^ 24) a000040_list) (map (^ 4) a006881_list) where
   m xs'@(x:xs) ys'@(y:ys) | x < y = x : m xs ys'
                           | otherwise = y : m xs' ys
-- Reinhard Zumkeller, Nov 29 2011
(PARI) is(n)=numdiv(n)==25 \\ Charles R Greathouse IV, Jun 19 2016

Crossrefs

Cf. A000005, A010812, A030513-A030516, A030626, A030627, A030634-A030638, A005179, A003680, A096932, A061286, A061283, A135581, A175755.

Sequence in context: A378768 A320893 A276282 * A189991 A250438 A221006

Adjacent sequences: A137485 A137486 A137487 * A137489 A137490 A137491

Keyword

nonn

Author

R. J. Mathar, Apr 22 2008

Status

approved