A320974 a(n) = n^n * Product_{p|n, p prime} (1 + 1/p^n).

1, 5, 28, 272, 3126, 47450, 823544, 16842752, 387440172, 10009766650, 285311670612, 8918294011904, 302875106592254, 11112685048647250, 437893920912786408, 18447025548686262272, 827240261886336764178, 39346558271492178663450, 1978419655660313589123980

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Wikipedia, Dedekind psi function

Formula

a(n) = [x^n] Sum_{k>=1} mu(k)^2*PolyLog(-n,x^k), where PolyLog() is the polylogarithm function.

a(n) = Sum_{d|n} mu(n/d)^2*d^n.

a(n) = A320973(n,n).

Mathematica

Table[n^n Product[1 + Boole[PrimeQ[d]]/d^n, {d, Divisors[n]}], {n, 19}]
Table[SeriesCoefficient[Sum[MoebiusMu[k]^2 PolyLog[-n, x^k], {k, 1, n}], {x, 0, n}], {n, 19}]
Table[Sum[MoebiusMu[n/d]^2 d^n, {d, Divisors[n]}], {n, 19}]

Crossrefs

Cf. A001615, A008683, A065958, A065959, A065960, A067858, A320973.

Sequence in context: A359700 A342677 A224607 * A339712 A023887 A171187

Adjacent sequences: A320971 A320972 A320973 * A320975 A320976 A320977

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 25 2018

Status

approved