A380049 Partial sums of A072203.

0, 1, 3, 4, 6, 7, 9, 12, 14, 15, 17, 20, 24, 27, 29, 30, 32, 35, 39, 44, 48, 51, 55, 58, 60, 61, 63, 66, 70, 75, 81, 88, 94, 99, 103, 106, 110, 113, 115, 116, 118, 121, 125, 130, 136, 141, 147, 154, 160, 167, 173, 180, 188, 195, 201, 206, 210, 213, 217, 220, 224, 227, 231, 234, 236

Offset: 1

Author

Tsuyoshi Hanatate, Jan 10 2025

Keywords

• nonn

Links

• Vaclav Kotesovec, Plot of a(n) / (2*n^(3/2)/(-3*zeta(1/2))) for n = 1..1000000

Crossrefs

Cf. A058933, A072203.

Programs

Mathematica

Accumulate[Accumulate[Table[-LiouvilleLambda[n], {n, 2, 100}]]] (* Vaclav Kotesovec, Jan 15 2025 *)

PARI

f(n) = 1 - sum(i=1, n, (-1)^bigomega(i)); \\ A072203
a(n) = sum(k=1, n, f(k)); \\ Michel Marcus, Feb 06 2025

Formula

a(n) = Sum_{k=1..n} A072203(k).

Conjecture: The average value of a(n) is 2*n^(3/2)/(-3*zeta(1/2)). - Vaclav Kotesovec, Jan 15 2025