A345266 a(n) = Sum_{p|n, p prime} gcd(p,n/p).
0, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 3, 2, 2, 1, 3, 5, 2, 3, 3, 1, 3, 1, 2, 2, 2, 2, 5, 1, 2, 2, 3, 1, 3, 1, 3, 4, 2, 1, 3, 7, 6, 2, 3, 1, 4, 2, 3, 2, 2, 1, 4, 1, 2, 4, 2, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 6, 3, 2, 3, 1, 3, 3, 2, 1, 4, 2, 2, 2, 3, 1, 5, 2, 3, 2, 2, 2, 3, 1, 8, 4, 7, 1, 3, 1, 3, 3
Offset: 1
Examples
a(18) = Sum_{p|18} gcd(p,18/p) = gcd(2,9) + gcd(3,6) = 1 + 3 = 4.
Links
Crossrefs
Programs
-
Mathematica
Table[Sum[GCD[k, 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), p); sum(k=1, #f~, p=f[k, 1]; gcd(p,n/p)); \\ Michel Marcus, Jun 16 2021
-
PARI
A345266(n) = vecsum(apply(p->gcd(p,n/p), factor(n)[,1])); \\ Antti Karttunen, Nov 13 2021
Formula
a(p) = 1 for p prime.
From Wesley Ivan Hurt, Nov 21 2021: (Start)
If n is squarefree, then a(n) = omega(n).
a(p^k) = p for primes p and k >= 2. (End)
Extensions
Data section extended up to 105 terms by Antti Karttunen, Nov 13 2021
Comments