A361064 Multiplicative with a(p^e) = sigma_3(e), where sigma_3 = A001158.

1, 1, 1, 9, 1, 1, 1, 28, 9, 1, 1, 9, 1, 1, 1, 73, 1, 9, 1, 9, 1, 1, 1, 28, 9, 1, 28, 9, 1, 1, 1, 126, 1, 1, 1, 81, 1, 1, 1, 28, 1, 1, 1, 9, 9, 1, 1, 73, 9, 9, 1, 9, 1, 28, 1, 28, 1, 1, 1, 9, 1, 1, 9, 252, 1, 1, 1, 9, 1, 1, 1, 252, 1, 1, 9, 9, 1, 1, 1, 73, 73, 1, 1, 9

Offset

1,4

Links

Table of n, a(n) for n=1..84.

Formula

Dirichlet g.f.: Product_{primes p} (1 + Sum_{e>=1} sigma_3(e) / p^(e*s)).

Sum_{k=1..n} a(k) ~ c * n, where c = Product_{p prime} (1 + Sum_{e>=2} (sigma_3(e) - sigma_3(e-1)) / p^e) = 136.775196585091127831467103699999450735835551529525277016916082455332230986...

Mathematica

g[p_, e_] := DivisorSigma[3, e]; a[1] = 1; a[n_] := Times @@ g @@@ FactorInteger[n]; Array[a, 100]

Prog

(Python)
from math import prod
from sympy import factorint, divisor_sigma
def A361064(n): return prod(divisor_sigma(e, 3) for e in factorint(n).values()) # Chai Wah Wu, Mar 01 2023

Crossrefs

Cf. A001158, A049419, A361012, A361063.

Cf. A327837, A361013.

Sequence in context: A293724 A283989 A361794 * A322029 A322107 A180839

Adjacent sequences: A361061 A361062 A361063 * A361065 A361066 A361067

Keyword

nonn,mult

Author

Vaclav Kotesovec, Mar 01 2023

Status

approved