A321236 a(n) = Sum_{d|n} mu(d)^2*d^n.

1, 5, 28, 17, 3126, 47450, 823544, 257, 19684, 10009766650, 285311670612, 2177317874, 302875106592254, 11112685048647250, 437893920912786408, 65537, 827240261886336764178, 101560344351050, 1978419655660313589123980, 100000095367432689202

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..388

Formula

G.f.: Sum_{k>=1} mu(k)^2*(k*x)^k/(1 - (k*x)^k).

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

Mathematica

Table[Sum[MoebiusMu[d]^2 d^n, {d, Divisors[n]}], {n, 20}]
nmax = 20; Rest[CoefficientList[Series[Sum[MoebiusMu[k]^2 (k x)^k/(1 - (k x)^k), {k, 1, nmax}], {x, 0, nmax}], x]]
Table[Product[1 + Boole[PrimeQ[d]] d^n, {d, Divisors[n]}], {n, 20}]

Prog

(PARI) a(n) = sumdiv(n, d, moebius(d)^2*d^n) \\ Andrew Howroyd, Nov 06 2018

Crossrefs

Cf. A008683, A048250, A320974, A321222.

Sequence in context: A351749 A016087 A347251 * A351774 A344579 A345263

Adjacent sequences: A321233 A321234 A321235 * A321237 A321238 A321239

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 06 2018

Status

approved