A229343 - OEIS

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A229343

Moebius function of the arithmetic derivative of n: a(n) = mu(n').

1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, -1, 1, 0, 1, 1, 0, 0, 1, -1, 1, 0, 1, -1, 0, 0, 1, 1, 0, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, -1, 1, 0, 1, 1, 1, 0, 0, -1, 1, 0, 1, -1, 1, 0, 1, 1, 1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 1

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OFFSET

LINKS

Antti Karttunen, Table of n, a(n) for n = 2..65537

FORMULA

a(n) = A008683(A003415(n)).

EXAMPLE

For n=4, mu(n') = mu(4') = mu(4) = 0.

For n=7, mu(n') = mu(7') = mu(1) = 1.

PROG

(PARI) rd(n) = {local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]; )); }

a(n) = moebius(rd(n)); \\ Michel Marcus, Sep 24 2013