login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
0

%I #11 Apr 01 2015 10:22:55

%S 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,

%T -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,

%U 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

%N 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.

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

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

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

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

%o (PARI) a(n) = moebius(n)*sum(k=1, n, kronecker(n, k)); \\ _Michel Marcus_, Mar 24 2015

%Y Cf. A008683, A071961.

%K sign

%O 1,6

%A _Robert G. Wilson v_, Mar 23 2015