A361064 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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