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A344194 a(n) = Sum_{k=1..n} tau(gcd(k,n))^gcd(k,n), where tau(n) is the number of divisors of n. 1
1, 5, 10, 87, 36, 4114, 134, 65629, 19705, 1048628, 2058, 2176786622, 8204, 268435614, 1073741928, 152587956347, 131088, 101559956696337, 524306, 3656158441111964, 4398046511420, 17592186046514, 8388630, 4722366482871822135514, 847288609591, 4503599627378748 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..26.

FORMULA

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

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

MATHEMATICA

a[n_] := DivisorSum[n, EulerPhi[n/#] * DivisorSigma[0, #]^# &]; Array[a, 26] (* Amiram Eldar, May 11 2021 *)

PROG

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

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

CROSSREFS

Cf. A000005, A342423, A344081, A344140, A344195.

Sequence in context: A317260 A111992 A325583 * A120598 A200983 A344140

Adjacent sequences:  A344191 A344192 A344193 * A344195 A344196 A344197

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 11 2021

STATUS

approved

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Last modified January 25 12:36 EST 2022. Contains 350572 sequences. (Running on oeis4.)