A262400 Let f(x) = 1 + Sum_{j>=4} (|mu(j)| - |mu(j-1)|)*x^j, where mu(n) is the Möbius function (A008683). Then a(n) is n times the coefficient of x^n in the expansion of log(f(x)).

0, 0, 0, 0, -4, 5, 0, 0, -12, 9, 5, 0, -28, 39, 0, -10, -60, 102, -45, 0, -119, 252, -132, 0, -252, 580, -403, 9, -424, 1363, -1210, 248, -828, 3003, -3332, 1195, -1729, 6697, -8740, 4290, -3807, 14514, -22176, 13889, -9288, 31049, -54142, 41501, -25260, 66885, -129570

Offset: 0

Author

Juan Arias-de-Reyna, Sep 21 2015

Keywords

• sign

Comments

Function f(x) is connected with the density h of the exponentially squarefree numbers (A209061). Specifically, for h = Product_{prime p} f(1/p), this sequence allows the calculation of h with very high accuracy (cf. A262276).

Links

• Juan Arias-de-Reyna, Table of n, a(n) for n = 0..3000

Crossrefs

Cf. A008683, A209061, A262276.

Programs

Mathematica

M = 50; (* to get the first 51 terms *)
f = 1 + Sum[(MoebiusMu[n]^2 - MoebiusMu[n - 1]^2) x^n, {n, 4, M}];
S = Series[Log[f], {x, 0, M}];
A262400[nn_] := CoefficientList[S, x][[nn + 1]] nn;
Table[A262400[n], {n, 0, M}]