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A320974
a(n) = n^n * Product_{p|n, p prime} (1 + 1/p^n).
2
1, 5, 28, 272, 3126, 47450, 823544, 16842752, 387440172, 10009766650, 285311670612, 8918294011904, 302875106592254, 11112685048647250, 437893920912786408, 18447025548686262272, 827240261886336764178, 39346558271492178663450, 1978419655660313589123980
OFFSET
1,2
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}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 25 2018
STATUS
approved