A294975 a(n) = (1/(24*n)) * Sum_{d|n} A008683(n/d) * (A288840(d) - A288877(d)).

30, 11775, 4261790, 1712983575, 733856931102, 327479190724415, 150310619778297630, 70428822637214055855, 33523597190372498303390, 16156445902947621421555071, 7865129058155113639991368350, 3860735065245244345161225213335

Offset: 1

Author

Seiichi Manyama, Feb 12 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..367

Crossrefs

Cf. A008683, A288840, A288877, A294976.

Programs

Mathematica

terms = 12;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E8[x_] = 1 + 480*Sum[k^7*x^k/(1 - x^k), {k, 1, terms}];
a[n_] := (1/(24 n))*Sum[MoebiusMu[n/d]*SeriesCoefficient[E8[x]/E6[x] - E4[x]/E2[x], {x, 0, d}], {d, Divisors[n]}];
Array[a, terms] (* Jean-François Alcover, Feb 26 2018 *)

Formula

a(n) ~ exp(2*Pi*n) / (12*n). - Vaclav Kotesovec, Jun 03 2018