login
a(n) = tau( sigma_n(n) ), where tau is the number of divisors of n.
3

%I #22 Apr 06 2022 15:32:03

%S 1,2,6,8,8,24,16,4,8,72,96,256,32,64,1728,64,12,384,48,2048,3456,128,

%T 512,2304,256,384,2048,9216,128,69120,384,2048,184320,2304,81920,2048,

%U 128,256,9216,1024,64,138240,384,16384,32768,3072,2560,131072,64,4194304,196608

%N a(n) = tau( sigma_n(n) ), where tau is the number of divisors of n.

%C Number of divisors of A023887(n).

%H Daniel Suteu, <a href="/A064165/b064165.txt">Table of n, a(n) for n = 1..120</a>

%e a(6) = 24; The sum of the 6th powers of the divisors of 6 is 1^6 + 2^6 + 3^6 + 6^6 = 47450, which has 24 divisors. - _Wesley Ivan Hurt_, May 04 2021

%t Table[DivisorSigma[0,DivisorSigma[w,w]],{w,30}] (* _Harvey P. Dale_, Jul 08 2019 *)

%o (PARI) a(n) = numdiv(sigma(n, n)); \\ _Michel Marcus_, May 05 2021

%o (Python)

%o from math import prod

%o from collections import Counter

%o from sympy import factorint

%o def A064165(n): return prod(r+1 for q,r in sum((Counter(factorint((p**(n*(e+1))-1)//(p**n-1))) for p, e in factorint(n).items()),Counter()).items()) # _Chai Wah Wu_, Jan 28 2022

%Y Cf. A000005 (tau), A000203 (sigma), A023887 (sigma_n(n)).

%K nonn

%O 1,2

%A _Labos Elemer_, Sep 19 2001

%E More terms from _Wesley Ivan Hurt_, May 04 2021