OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..385
FORMULA
a(n) = [x^n] Sum_{i>=1} Sum_{j>=1} mu(i)*j^(n+1)*x^(i*j)/(1 - x^(i*j))^2.
a(n) = Sum_{d|n} phi(n/d)*d^(n+1).
a(n) = Sum_{k=1..n} gcd(n,k)^(n+1).
a(n) ~ n^(n+1). - Vaclav Kotesovec, Nov 02 2018
MATHEMATICA
Table[Sum[MoebiusMu[n/d] d DivisorSigma[n, d], {d, Divisors[n]}], {n, 18}]
Table[Sum[EulerPhi[n/d] d^(n + 1), {d, Divisors[n]}], {n, 18}]
Table[Sum[GCD[n, k]^(n + 1), {k, n}], {n, 18}]
PROG
(PARI) a(n) = sumdiv(n, d, moebius(n/d)*d*sigma(d, n)); \\ Michel Marcus, Nov 03 2018
(Python)
from sympy import totient, divisors
def A321294(n):
return sum(totient(d)*(n//d)**(n+1) for d in divisors(n, generator=True)) # Chai Wah Wu, Feb 15 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 02 2018
STATUS
approved