A030232 - OEIS

%I #17 May 21 2022 08:42:05

%S 1,2,4,8,10,13,20,22,24,32,33,34,37,42,56,68,75,100,102,108,114,129,

%T 133,134,136,148,149,153,159,161,162,186,187,248,249,254,277,300,301,

%U 310,311,330,331,351,380,381,382,388,411,423,430,488,489,531,545,556

%N Numbers k such that the number of divisors of k! divides the number of divisors of (2k)!.

%C Numbers k such that A000005(k!) divides A000005((2k)!).

%H Amiram Eldar, <a href="/A030232/b030232.txt">Table of n, a(n) for n = 1..121</a>

%t Select[Range[560],Divisible[DivisorSigma[0,(2#)!],DivisorSigma[ 0,#!]]&] (* _Harvey P. Dale_, Mar 06 2015 *)

%o (PARI) isok(n) = (numdiv((2*n)!) % numdiv(n!)) == 0; \\ _Michel Marcus_, Apr 16 2015

%Y Cf. A000005 (number of divisors), A027423 (number of divisors of n!).

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Sep 28 2002