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A064165 a(n) = tau( sigma_n(n) ), where tau is the number of divisors of n.

%I A064165 #22 Apr 06 2022 15:32:03
%S A064165 1,2,6,8,8,24,16,4,8,72,96,256,32,64,1728,64,12,384,48,2048,3456,128,
%T A064165 512,2304,256,384,2048,9216,128,69120,384,2048,184320,2304,81920,2048,
%U A064165 128,256,9216,1024,64,138240,384,16384,32768,3072,2560,131072,64,4194304,196608
%N A064165 a(n) = tau( sigma_n(n) ), where tau is the number of divisors of n.
%C A064165 Number of divisors of A023887(n).
%H A064165 Daniel Suteu, <a href="/A064165/b064165.txt">Table of n, a(n) for n = 1..120</a>
%e A064165 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 A064165 Table[DivisorSigma[0,DivisorSigma[w,w]],{w,30}] (* _Harvey P. Dale_, Jul 08 2019 *)
%o A064165 (PARI) a(n) = numdiv(sigma(n, n)); \\ _Michel Marcus_, May 05 2021
%o A064165 (Python)
%o A064165 from math import prod
%o A064165 from collections import Counter
%o A064165 from sympy import factorint
%o A064165 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 A064165 Cf. A000005 (tau), A000203 (sigma), A023887 (sigma_n(n)).
%K A064165 nonn
%O A064165 1,2
%A A064165 _Labos Elemer_, Sep 19 2001
%E A064165 More terms from _Wesley Ivan Hurt_, May 04 2021