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Numbers with 39 divisors.
3

%I #21 Jul 03 2022 06:46:29

%S 36864,102400,200704,495616,692224,1183744,1478656,2125764,2166784,

%T 3444736,3936256,5607424,6885376,7573504,9048064,11505664,13286025,

%U 14258176,15241216,18386944,20647936,21827584,25563136,26040609,28217344,32444416,38539264,41783296

%N Numbers with 39 divisors.

%C Numbers of the forms p^38 and p^12*q^2, where p and q are distinct primes.

%H T. D. Noe, <a href="/A175748/b175748.txt">Table of n, a(n) for n = 1..1000</a>

%H OEIS Wiki, <a href="https://oeis.org/wiki/Index_entries_for_number_of_divisors">Index entries for number of divisors</a>

%F A000005(a(n)) = 39.

%F Sum_{n>=1} 1/a(n) = P(2)*P(12) - P(14) + P(38) = 0.0000500204..., where P is the prime zeta function. - _Amiram Eldar_, Jul 03 2022

%t Select[Range[7000000],DivisorSigma[0,#]==39&] (* _Vladimir Joseph Stephan Orlovsky_, May 06 2011 *)

%o (PARI) is(n)=numdiv(n)==39 \\ _Charles R Greathouse IV_, Jun 19 2016

%Y Cf. A000005, A139572, A175747.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Aug 27 2010

%E Extended by _T. D. Noe_, May 08 2011