login
Number of divisors function applied twice to n!.
2

%I #17 May 01 2016 16:48:41

%S 1,2,3,4,5,8,12,12,12,16,24,24,30,30,42,36,40,48,56,80,48,72,80,112,

%T 112,144,120,216,252,168,189,168,80,224,168,288,320,121,192,440,480,

%U 384,408,624,792,864,960,1152,864,728,504,780,840,1080,960,840,972

%N Number of divisors function applied twice to n!.

%H Ivan Neretin, <a href="/A053021/b053021.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A010553(n!) = A000005(A027423(n)) = A000005(A000005(A000142(n))).

%e a(7) = d(d(7!)) = d(60) = 12;

%e a(8) = d(d(8!)) = d(96) = 12.

%t DivisorSigma[0,DivisorSigma[0,Range[60]!]] (* _Harvey P. Dale_, May 20 2013 *)

%o (PARI) a(n) = numdiv(numdiv(n!)); \\ _Michel Marcus_, May 01 2016

%Y Cf. A000005, A000142, A027423, A010553.

%K nonn

%O 1,2

%A _Labos Elemer_, Feb 24 2000