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

1, 2, 6, 8, 8, 24, 16, 4, 8, 72, 96, 256, 32, 64, 1728, 64, 12, 384, 48, 2048, 3456, 128, 512, 2304, 256, 384, 2048, 9216, 128, 69120, 384, 2048, 184320, 2304, 81920, 2048, 128, 256, 9216, 1024, 64, 138240, 384, 16384, 32768, 3072, 2560, 131072, 64, 4194304, 196608

Offset: 1

Author

Labos Elemer, Sep 19 2001

Keywords

• nonn

Comments

Number of divisors of A023887(n).

Examples

			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
		

Links

• Daniel Suteu, Table of n, a(n) for n = 1..120

Crossrefs

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

Programs

Mathematica

Table[DivisorSigma[0,DivisorSigma[w,w]],{w,30}] (* Harvey P. Dale, Jul 08 2019 *)

PARI

a(n) = numdiv(sigma(n, n)); \\ Michel Marcus, May 05 2021

Python

from math import prod
from collections import Counter
from sympy import factorint
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

Extensions

More terms from Wesley Ivan Hurt, May 04 2021