A345355 a(n) = Sum_{p|n, p prime} p^omega(n/p).
0, 1, 1, 2, 1, 5, 1, 2, 3, 7, 1, 7, 1, 9, 8, 2, 1, 11, 1, 9, 10, 13, 1, 7, 5, 15, 3, 11, 1, 38, 1, 2, 14, 19, 12, 13, 1, 21, 16, 9, 1, 62, 1, 15, 14, 25, 1, 7, 7, 27, 20, 17, 1, 11, 16, 11, 22, 31, 1, 42, 1, 33, 16, 2, 18, 134, 1, 21, 26, 78, 1, 13, 1, 39, 28, 23, 18, 182
Offset: 1
Keywords
Examples
a(30) = Sum_{p|30} p^omega(30/p) = 2^omega(15) + 3^omega(10) + 5^omega(6) = 2^2 + 3^2 + 5^2 = 38.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..20000
Programs
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Mathematica
Table[Sum[k^PrimeNu[n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}] -
PARI
a(n) = my(f=factor(n)); sum(k=1, #f~, f[k,1]^omega(n/f[k,1])); \\ Michel Marcus, Jun 16 2021
Formula
a(p) = 1 for p prime.
a(n) = Sum_{d|n} d^omega(n/d) * c(d), where c = A010051. - Wesley Ivan Hurt, Apr 13 2025
Comments