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

Author

Seiichi Manyama, May 12 2021

Keywords

• nonn

Links

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

Crossrefs

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

Programs

Mathematica

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

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);

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.