A262400 - OEIS

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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

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OFFSET

0,5

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

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}]

CROSSREFS

Cf. A008683, A209061, A262276.

Sequence in context: A335762 A254294 A143574 * A075424 A200619 A199621

Adjacent sequences: A262397 A262398 A262399 * A262401 A262402 A262403

KEYWORD

sign

AUTHOR

Juan Arias-de-Reyna, Sep 21 2015

STATUS

approved