A330324 a(n) = Sum_{i=1..n} Moebius(i)*Moebius(i+1), where Moebius(n) = A008683(n).

-1, 0, 0, 0, -1, -2, -2, -2, -2, -3, -3, -3, -4, -3, -3, -3, -3, -3, -3, -3, -2, -3, -3, -3, -3, -3, -3, -3, -2, -1, -1, -1, 0, 1, 1, 1, 0, 1, 1, 1, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, -1, 0, 1, 1

Offset

1,6

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Maple

a:= proc(n) option remember; `if`(n<1, 0,
      a(n-1)+numtheory[mobius](n*(n+1)))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Apr 17 2021

Mathematica

Accumulate @ Table[MoebiusMu[n] * MoebiusMu[n+1], {n, 1, 100}] (* Amiram Eldar, Jul 26 2022 *)

Prog

(PARI) a(n) = sum(i=1, n, moebius(i*(i+1))); \\ Michel Marcus, Jul 26 2022

Crossrefs

Partial sums of A330323.

Cf. A008683.

Sequence in context: A054893 A090617 A053693 * A341132 A291309 A280472

Adjacent sequences: A330321 A330322 A330323 * A330325 A330326 A330327

Keyword

sign

Author

N. J. A. Sloane, Dec 12 2019

Status

approved