A344226 a(n) = Sum_{d|n} n^omega(d) / d.

1, 2, 2, 4, 2, 12, 2, 8, 5, 18, 2, 50, 2, 24, 24, 16, 2, 90, 2, 80, 32, 36, 2, 198, 7, 42, 14, 110, 2, 1232, 2, 32, 48, 54, 48, 476, 2, 60, 56, 324, 2, 2310, 2, 170, 210, 72, 2, 782, 9, 338, 72, 200, 2, 756, 72, 450, 80, 90, 2, 12558, 2, 96, 290, 64, 84, 5474, 2, 260, 96, 5940

Offset: 1

Author

Seiichi Manyama, May 12 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A062319, A344223.

Programs

Mathematica

Table[DivisorSum[n,n^PrimeNu@#/#&],{n,100}] (* Giorgos Kalogeropoulos, May 13 2021 *)

PARI

a(n) = sumdiv(n, d, n^omega(d)/d);

PARI

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

PARI

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

Formula

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

a(n) = (1/n) * Sum_{d|n} phi(n/d) * tau(d^n).

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