A369869 a(n) = n * Sum_{p|n, p prime} pi(n/p) / p.

0, 0, 0, 2, 0, 8, 0, 8, 6, 17, 0, 26, 0, 30, 21, 32, 0, 54, 0, 48, 34, 57, 0, 92, 15, 80, 36, 92, 0, 148, 0, 96, 61, 121, 43, 186, 0, 154, 84, 192, 0, 270, 0, 184, 126, 209, 0, 312, 28, 265, 125, 242, 0, 369, 70, 284, 158, 292, 0, 520, 0, 343, 204, 352, 93, 557, 0

Offset

1,4

Comments

Dirichlet convolution of c(n) and n*pi(n), where c = A010051. - Wesley Ivan Hurt, Jun 24 2026

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(p^k) = p^(k-1) * pi(p^(k-1)), for prime p and k >= 1. - Wesley Ivan Hurt, Jun 26 2024

a(n) = Sum_{d|n} d*pi(d)*c(n/d), where c = A010051. - Wesley Ivan Hurt, Jun 24 2026

Mathematica

Table[n*DivisorSum[n, PrimePi[n/#]/# &, PrimeQ[#] &], {n, 100}]

Prog

(PARI) A369869(n) = if(1==n, 0, n*my(f=factor(n)); n*sum(i=1, #f~, primepi(n/f[i, 1])/f[i, 1])); \\ Antti Karttunen, Jan 22 2025

Crossrefs

Cf. A000720 (pi), A010051, A345301, A369745, A369747, A369868.

Sequence in context: A348510 A200489 A011124 * A011250 A073830 A213272

Adjacent sequences: A369866 A369867 A369868 * A369870 A369871 A369872

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Feb 03 2024

Status

approved