OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
FORMULA
Dirichlet g.f.: Product_{primes p} 1 / (1 - p^(1-s) - 4*p^(-s)).
Dirichlet g.f.: zeta(s-1) * (1 + 4/(2^s - 6)) * Product_{primes p, p>2} (1 + 4/(p^s - p - 4)).
Sum_{k=1..n} a(k) has an average value 2*c*zeta(r-1) * n^r / (3*log(6)), where r = 1 + log(3)/log(2) = 2.5849625007211561814537389439478165... and c = Product_{primes p, p>2} (1 + 4/(p^r - p - 4)) = 1.5747380964592139...
MATHEMATICA
g[p_, e_] := (p + 4)^e; a[1] = 1; a[n_] := Times @@ g @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) for(n=1, 100, print1(direuler(p=2, n, 1/(1-p*X-4*X))[n], ", "))
(Python)
from math import prod
from sympy import factorint
def A359530(n): return prod((p+4)**e for p, e in factorint(n).items()) # Chai Wah Wu, Feb 26 2023
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Vaclav Kotesovec, Feb 26 2023
STATUS
approved