A253179 - OEIS

A253179

a(n) = mu(n)*Sum_{k=1..n} (n/k) where mu(n) is Möbius (or Moebius) function and (x/y) is Kronecker's symbol.

1, -1, 0, 0, 0, 2, -4, 0, 0, 2, -2, 0, 0, 4, 6, 0, 0, 0, -2, 0, 0, 2, -6, 0, 0, 6, 0, 0, 0, -4, -12, 0, 0, 4, 4, 0, 0, 6, 12, 0, 0, -4, 0, 0, 0, 4, -10, 0, 0, 0, 4, 0, 0, 0, 18, 0, 0, 2, -6, 0, 0, 8, 0, 0, 0, -8, 2, 0, 0, -4, -14, 0, 0, 10, 0, 0, 0, -4, -22, 0, 0, 4, -4, 0, 0, 10, 14, 0, 0, 0, 2, 0, 0, 8, 14, 0, 0, 0, 0, 0, 0, -4, -22, 0, 0

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OFFSET

1,6

COMMENTS

Conjecture: the partial sum of this sequence changes sign infinitely often.

All terms are congruent to 0 (mod 2) for n>2.

LINKS

Table of n, a(n) for n=1..105.

FORMULA

a(n) = A008683(n)*A071961(n).

MATHEMATICA

f[n_] := MoebiusMu[n] * Sum[ KroneckerSymbol[n, k], {k, n}]; Array[f, 100]