A321265 a(n) = [x^n] Product_{k>=1} (1 + x^k)^J_n(k), where J_() is the Jordan function.

1, 1, 3, 33, 425, 12083, 665707, 68834806, 13654633905, 5535319947544, 4371956013518511, 6700051541666225780, 21029477920140943174285, 131152064162504305814647983, 1603485136950993248524876767297, 40291404321882574322412345562762188, 2031269423141309839019651314585293713041

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Wikipedia, Jordan's totient function

Formula

a(n) = [x^n] exp(Sum_{k>=1} ( Sum_{d|k} Sum_{j|d} (-1)^(k/d+1)*d*j^n*mu(d/j) ) * x^k/k).

Mathematica

Table[SeriesCoefficient[Product[(1 + x^k)^Sum[d^n MoebiusMu[k/d], {d, Divisors[k]}], {k, 1, n}], {x, 0, n}], {n, 0, 16}]
Table[SeriesCoefficient[Exp[Sum[Sum[Sum[(-1)^(k/d + 1) d j^n MoebiusMu[d/j], {j, Divisors[d]}], {d, Divisors[k]}] x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 16}]

Crossrefs

Cf. A059379, A059380, A299069, A301876, A321042, A321264.

Sequence in context: A294167 A009502 A222941 * A011922 A365028 A368442

Adjacent sequences: A321262 A321263 A321264 * A321266 A321267 A321268

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 01 2018

Status

approved