A344224 a(n) = Sum_{k=1..n} tau(gcd(k,n)^gcd(k,n)), where tau(n) is the number of divisors of n.

1, 4, 6, 14, 10, 61, 14, 44, 33, 143, 22, 410, 26, 257, 292, 128, 34, 852, 38, 1050, 536, 581, 46, 2352, 95, 791, 162, 1978, 58, 30545, 62, 352, 1240, 1307, 1388, 6918, 74, 1613, 1700, 6264, 82, 80823, 86, 4698, 4866, 2321, 94, 12416, 189, 5790, 2836, 6490, 106, 10881, 3284, 12032, 3512, 3623

Offset

1,2

Links

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

Formula

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

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

Mathematica

Table[Sum[DivisorSigma[0, GCD[k, n]^(GCD[k, n])], {k, n}], {n, 100}] (* Giorgos Kalogeropoulos, May 13 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. A344221, A344222, A344223, A344225.

Sequence in context: A253535 A349171 A338658 * A310601 A310602 A296910

Adjacent sequences: A344221 A344222 A344223 * A344225 A344226 A344227

Keyword

nonn

Author

Seiichi Manyama, May 12 2021

Status

approved