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A344140 a(n) = Sum_{x_1|n, x_2|n, ... , x_n|n} gcd(x_1,x_2, ... ,x_n). 8
1, 5, 10, 99, 36, 4290, 134, 72613, 20713, 1053700, 2058, 2194638822, 8204, 268550150, 1073938440, 156969213515, 131088, 101697785139535, 524306, 3657271905119820, 4398063288332, 17592232181770, 8388630, 4727105990672866963914, 847422827191, 4503600499785740 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..719

FORMULA

a(n) = Sum_{x_1|n, x_2|n, ... , x_n|n} n/lcm(x_1,x_2, ... ,x_n).

a(n) = Sum_{d|n} phi(n/d) * tau(d)^n.

If p is prime, a(p) = 2^p - 1 + p.

a(n) = Sum_{k=1..n} tau(gcd(k,n))^n.

MATHEMATICA

a[n_] := DivisorSum[n, EulerPhi[n/#] * DivisorSigma[0, #]^n &]; Array[a, 20] (* Amiram Eldar, May 10 2021 *)

PROG

(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*numdiv(d)^n);

(PARI) a(n) = sum(k=1, n, numdiv(gcd(k, n))^n);

CROSSREFS

Cf. A000203, A060724, A344080, A344132, A344138, A344139.

Sequence in context: A344194 A120598 A200983 * A267042 A119137 A048360

Adjacent sequences:  A344137 A344138 A344139 * A344141 A344142 A344143

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 10 2021

STATUS

approved

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Last modified January 17 14:42 EST 2022. Contains 350401 sequences. (Running on oeis4.)