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URL: https://oeis.org/A321294

⇱ A321294 - OEIS

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A321294
a(n) = Sum_{d|n} mu(n/d)*d*sigma_n(d).
3
1, 9, 83, 1058, 15629, 282381, 5764807, 134480900, 3486902505, 100048836321, 3138428376731, 107006403495850, 3937376385699301, 155572843119518781, 6568408661060858767, 295150157013526773768, 14063084452067724991025, 708236697425777157039381
OFFSET
1,2
LINKS
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