cp's OEIS Frontend

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

%I A294975 #17 Jun 03 2018 09:31:27
%S A294975 30,11775,4261790,1712983575,733856931102,327479190724415,
%T A294975 150310619778297630,70428822637214055855,33523597190372498303390,
%U A294975 16156445902947621421555071,7865129058155113639991368350,3860735065245244345161225213335
%N A294975 a(n) = (1/(24*n)) * Sum_{d|n} A008683(n/d) * (A288840(d) - A288877(d)).
%H A294975 Seiichi Manyama, <a href="/A294975/b294975.txt">Table of n, a(n) for n = 1..367</a>
%F A294975 a(n) ~ exp(2*Pi*n) / (12*n). - _Vaclav Kotesovec_, Jun 03 2018
%t A294975 terms = 12;
%t A294975 E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
%t A294975 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A294975 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t A294975 E8[x_] = 1 + 480*Sum[k^7*x^k/(1 - x^k), {k, 1, terms}];
%t A294975 a[n_] := (1/(24 n))*Sum[MoebiusMu[n/d]*SeriesCoefficient[E8[x]/E6[x] - E4[x]/E2[x], {x, 0, d}], {d, Divisors[n]}];
%t A294975 Array[a, terms] (* _Jean-François Alcover_, Feb 26 2018 *)
%Y A294975 Cf. A008683, A288840, A288877, A294976.
%K A294975 nonn
%O A294975 1,1
%A A294975 _Seiichi Manyama_, Feb 12 2018