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
Links
- Antti Karttunen, Table of n, a(n) for n = 1..20000
Programs
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Mathematica
Table[n*DivisorSum[n, PrimePi[n/#]/# &, PrimeQ[#] &], {n, 100}] -
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
Formula
a(p^k) = p^(k-1) * pi(p^(k-1)), for prime p and k >= 1. - Wesley Ivan Hurt, Jun 26 2024