A361063 Multiplicative with a(p^e) = sigma_2(e), where sigma_2 = A001157.

1, 1, 1, 5, 1, 1, 1, 10, 5, 1, 1, 5, 1, 1, 1, 21, 1, 5, 1, 5, 1, 1, 1, 10, 5, 1, 10, 5, 1, 1, 1, 26, 1, 1, 1, 25, 1, 1, 1, 10, 1, 1, 1, 5, 5, 1, 1, 21, 5, 5, 1, 5, 1, 10, 1, 10, 1, 1, 1, 5, 1, 1, 5, 50, 1, 1, 1, 5, 1, 1, 1, 50, 1, 1, 5, 5, 1, 1, 1, 21, 21, 1, 1, 5

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_2(e) / p^(e*s)).

Sum_{k=1..n} a(k) ~ c * n, where c = Product_{p prime} (1 + Sum_{e>=2} (sigma_2(e) - sigma_2(e-1)) / p^e) = 11.343154585178523783556367128387762286267199879648613456124659589127638983...

Mathematica

g[p_, e_] := DivisorSigma[2, 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 A361063(n): return prod(divisor_sigma(e, 2) for e in factorint(n).values()) # Chai Wah Wu, Mar 01 2023

Crossrefs

Cf. A001157, A049419, A361012, A361064.

Cf. A327837, A361013.

Sequence in context: A140210 A360720 A010130 * A363972 A206773 A229526

Adjacent sequences: A361060 A361061 A361062 * A361064 A361065 A361066

Keyword

nonn,mult

Author

Vaclav Kotesovec, Mar 01 2023

Status

approved