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

1,2

Comments

Number of divisors of A023887(n).

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A093888 A136702 A328910 * A320573 A003610 A201776

Adjacent sequences: A064162 A064163 A064164 * A064166 A064167 A064168

Keyword

nonn

Author

Labos Elemer, Sep 19 2001

Extensions

More terms from Wesley Ivan Hurt, May 04 2021

Status

approved