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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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A018804, A069097, A320940, A332517, A342432, A342433.

Sequence in context: A162759 A147960 A155499 * A242596 A180807 A203455

Adjacent sequences:  A321291 A321292 A321293 * A321295 A321296 A321297

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 02 2018

STATUS

approved

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Last modified June 15 08:14 EDT 2021. Contains 345048 sequences. (Running on oeis4.)