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A064165
a(n) = tau( sigma_n(n) ), where tau is the number of divisors of n.
3
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 19 2001
EXTENSIONS
More terms from Wesley Ivan Hurt, May 04 2021
STATUS
approved