A112399 - OEIS

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A112399

a(n) = Sum_{k=1..n, gcd(k,n)=1} mu(k), where mu(k) = A008683(k) (the Moebius function).

1, 1, 0, 0, -1, 0, -1, -2, -2, -1, -1, -2, -2, -3, -2, -3, -1, -4, -2, -5, -4, -3, -1, -6, -3, -4, -3, -5, -1, -6, -3, -7, -5, -5, -3, -7, -1, -5, -3, -6, 0, -9, -2, -7, -6, -6, -2, -11, -4, -9, -5, -7, -2, -12, -5, -8, -5, -5, 0, -13, -1, -7, -6, -8, -4, -12, -1, -8, -5, -10, -2, -14, -3, -8, -9, -9, -4, -14, -3, -12, -7, -8, -3, -17

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,8

LINKS

Table of n, a(n) for n=1..84.

EXAMPLE

The positive integers <= 10 and coprime to 10 are 1, 3, 7 and 9. So a(10) = mu(1) + mu(3) + mu(7) + mu(9) = 1 - 1 - 1 + 0 = -1.

MATHEMATICA

quetMu[n_] := Sum[KroneckerDelta[GCD[i, n], 1] MoebiusMu[i], {i, n}]; Table[quetMu[n], {n, 85}] (* Alonso del Arte, Nov 28 2011 *)

PROG

(PARI) a(n)=sum(k=1, n, if(gcd(n, k)==1, moebius(k), 0)) \\ Lambert Herrgesell, Dec 09 2005

CROSSREFS