%I #9 Mar 01 2023 11:28:47

%S 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,

%T 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,

%U 9,252,1,1,1,9,1,1,1,252,1,1,9,9,1,1,1,73,73,1,1,9

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

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

%F 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...

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

%o (Python)

%o from math import prod

%o from sympy import factorint, divisor_sigma

%o def A361064(n): return prod(divisor_sigma(e,3) for e in factorint(n).values()) # _Chai Wah Wu_, Mar 01 2023

%Y Cf. A001158, A049419, A361012, A361063.

%Y Cf. A327837, A361013.

%K nonn,mult

%O 1,4

%A _Vaclav Kotesovec_, Mar 01 2023