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

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]

Prog

(PARI) a(n) = moebius(n)*sum(k=1, n, kronecker(n, k)); \\ Michel Marcus, Mar 24 2015

Crossrefs

Cf. A008683, A071961.

Sequence in context: A371648 A347679 A028586 * A300723 A263788 A355335

Adjacent sequences: A253176 A253177 A253178 * A253180 A253181 A253182

Keyword

sign

Author

Robert G. Wilson v, Mar 23 2015

Status

approved