A373004 a(n) = Sum_{k=1..n} sigma( (n/gcd(k,n))^n ).

1, 8, 81, 1054, 15625, 279936, 5764801, 134480378, 3486843447, 100000000000, 3138428376721, 107006262884442, 3937376385699289, 155568095557812224, 6568408355712890625, 295150156996346511346, 14063084452067724991009, 708235345964697414795264

Offset

1,2

Links

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

Formula

If k is squarefree (cf. A005117) then a(k) = k^(k+1).

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

Prog

(PARI) a(n) = sumdiv(n, d, eulerphi(d)*sigma(d^n));

Crossrefs

Cf. A062952, A372227, A372998, A373000.

Cf. A005117, A007778.

Sequence in context: A338694 A318047 A338685 * A092366 A022519 A138439

Adjacent sequences: A373001 A373002 A373003 * A373005 A373006 A373007

Keyword

nonn

Author

Seiichi Manyama, May 19 2024

Status

approved