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A137490 Numbers with 27 divisors. 1

%I #22 Jul 03 2022 06:46:56

%S 900,1764,2304,4356,4900,6084,6400,10404,11025,12100,12544,12996,

%T 16900,19044,23716,26244,27225,28900,30276,30976,33124,34596,36100,

%U 38025,43264,49284,52900,53361,56644,60516,65025,66564,70756,73984,74529

%N Numbers with 27 divisors.

%C Maple implementation: see A030513.

%C Numbers of the form p^26 (subset of A089081), p^2*q^2*r^2 (like 900, 1764, 4356, squares of A007304) or p^2*q^8 (like 2304, 6400, subset of the squares of A030628) where p, q and r are distinct primes. - _R. J. Mathar_, Mar 01 2010

%H Vincenzo Librandi, <a href="/A137490/b137490.txt">Table of n, a(n) for n = 1..1000</a>

%F A000005(a(n)) = 27.

%F Sum_{n>=1} 1/a(n) = (P(2)^3 + 2*P(6) - 3*P(2)*P(4))/6 + P(2)*P(8) - P(10) + P(26) = 0.00453941..., where P is the prime zeta function. - _Amiram Eldar_, Jul 03 2022

%t Select[Range[150000],DivisorSigma[0,#]==27&] (* _Vladimir Joseph Stephan Orlovsky_, May 06 2011 *)

%o (PARI) isA137490(n) = numdiv(n)==27 \\ _Michael B. Porter_, Apr 10 2010

%Y Cf. A000005, A030513-A030516, A030626, A030627, A030634-A030638, A005179, A003680, A096932, A061286, A061283.

%K nonn

%O 1,1

%A _R. J. Mathar_, Apr 22 2008

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)