A372700 a(n) = Sum_{j=1..n} Sum_{k=1..n} mu(j*k), where mu is the Moebius function A008683.

1, -1, -1, -1, 1, 1, 3, 3, 3, 1, 3, 3, 7, 1, -3, -3, -1, -1, 3, 3, -5, -11, -9, -9, -9, -17, -17, -17, -15, -3, 3, 3, -7, -17, -23, -23, -21, -31, -37, -37, -37, -19, -15, -15, -15, -27, -23, -23, -23, -23, -33, -33, -29, -29, -39, -39, -49, -59, -59, -59, -57, -71, -71, -71, -79, -55, -53, -53, -63, -43, -39, -39

Offset

1,7

Comments

Conjecture: a(n) changes sign infinitely often.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

If n is not squarefree, a(n) = a(n-1).

a(n) = -1 + 2 * Sum_{k=1..n} A372706(k).

Prog

(PARI) a(n) = sum(j=1, n, sum(k=1, n, moebius(j*k)));

Crossrefs

Cf. A002321, A008683, A013929, A372706.

Sequence in context: A153401 A181520 A256736 * A123073 A059289 A201277

Adjacent sequences: A372696 A372698 A372699 * A372701 A372702 A372703

Keyword

sign,look

Author

Seiichi Manyama, May 10 2024

Status

approved