A362029 a(n) = Sum_{k=1..n} (-1)^(n-k) * k * mu(k)^2, where mu(k) is the Moebius function.

1, 1, 2, -2, 7, -1, 8, -8, 8, 2, 9, -9, 22, -8, 23, -23, 40, -40, 59, -59, 80, -58, 81, -81, 81, -55, 55, -55, 84, -54, 85, -85, 118, -84, 119, -119, 156, -118, 157, -157, 198, -156, 199, -199, 199, -153, 200, -200, 200, -200, 251, -251, 304, -304, 359, -359, 416, -358, 417, -417, 478, -416, 416

Offset

1,3

Links

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

Formula

G.f.: (Sum_{k>=1} mu(k)^2 * k * x^k) / (1 + x).

a(n) = -a(n-1) + |A055615(n)| for n > 1.

Prog

(PARI) a(n) = sum(k=1, n, (-1)^(n-k)*k*moebius(k)^2);

Crossrefs

Cf. A008683, A066779, A055615, A362021, A362028.

Sequence in context: A190256 A013671 A019807 * A324085 A340180 A063706

Adjacent sequences: A362026 A362027 A362028 * A362030 A362031 A362032

Keyword

sign,easy

Author

Seiichi Manyama, Apr 05 2023

Status

approved