A347104 Dirichlet g.f.: primezeta(s-1) * zeta(s-1) / zeta(s).
0, 2, 3, 2, 5, 7, 7, 4, 6, 13, 11, 10, 13, 19, 22, 8, 17, 18, 19, 18, 32, 31, 23, 20, 20, 37, 18, 26, 29, 38, 31, 16, 52, 49, 58, 24, 37, 55, 62, 36, 41, 56, 43, 42, 54, 67, 47, 40, 42, 60, 82, 50, 53, 54, 94, 52, 92, 85, 59, 60, 61, 91, 78, 32, 112, 92, 67, 66, 112, 106, 71, 48, 73, 109, 100
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
-
Mathematica
Table[DivisorSum[n, MoebiusMu[n/#] # PrimeNu[#] &], {n, 1, 75}] Table[DivisorSum[n, # EulerPhi[n/#] &, PrimeQ[#] &], {n, 1, 75}] Table[Sum[Boole[PrimeQ[GCD[n, k]]] GCD[n, k], {k, 1, n}], {n, 1, 75}] -
PARI
a(n) = sumdiv(n, d, moebius(n/d)*d*omega(d)); \\ Michel Marcus, Aug 18 2021
Formula
a(n) = Sum_{d|n} mu(n/d) * d * omega(d).
a(n) = Sum_{p|n, p prime} p * phi(n/p).
a(n) = Sum_{k=1..n} A010051(gcd(n,k)) * gcd(n,k).
Comments