A344223 a(n) = Sum_{k=1..n} tau(gcd(k,n)^n), where tau(n) is the number of divisors of n.

1, 4, 6, 16, 10, 72, 14, 64, 45, 180, 22, 600, 26, 336, 360, 256, 34, 1620, 38, 1600, 672, 792, 46, 4752, 175, 1092, 378, 3080, 58, 36960, 62, 1024, 1584, 1836, 1680, 17136, 74, 2280, 2184, 12960, 82, 97020, 86, 7480, 9450, 3312, 94, 37536, 441, 16900, 3672, 10400, 106, 40824, 3960, 25200

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

a(n) = n * A344226(n).

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

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

If p is prime, a(p) = 2*p.

Mathematica

Table[Sum[DivisorSigma[0, GCD[k, n]^n], {k, n}], {n, 100}] (* Giorgos Kalogeropoulos, May 13 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, numdiv(gcd(k, n)^n));
(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*numdiv(d^n));
(PARI) a(n) = n*sumdiv(n, d, n^omega(d)/d);

Crossrefs

Cf. A000203, A332517, A344221, A344222, A344224, A344225, A344226.

Sequence in context: A062955 A174932 A359103 * A347263 A347186 A278239

Adjacent sequences: A344220 A344221 A344222 * A344224 A344225 A344226

Keyword

nonn

Author

Seiichi Manyama, May 12 2021

Status

approved