A372939 a(n) = Sum_{1 <= x_1, x_2, ... , x_n <= n} gcd(x_1, x_2, ... , x_n, n)^n.

1, 7, 53, 736, 6249, 185039, 1647085, 66912256, 1162222101, 39980466703, 570623341221, 53487845236736, 605750213184505, 44446670856053599, 1751575500459583437, 92232594468640915456, 1654480523772673528353, 236077997761634282622495

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = Sum_{d|n} mu(n/d) * d^n * tau(d), where mu is the Moebius function A008683.

Prog

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

Crossrefs

Main diagonal of A372938.

Cf. A000005, A008683.

Sequence in context: A092802 A062207 A073564 * A194929 A317689 A116202

Adjacent sequences: A372936 A372937 A372938 * A372940 A372941 A372942

Keyword

nonn

Author

Seiichi Manyama, May 17 2024

Status

approved