A345374 Number of unitary prime divisors of n whose prime index is odd.
0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 2, 1, 0, 0, 1, 0, 0, 0, 2, 1, 0, 1, 2, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 1, 1, 0, 2, 0, 0, 1, 2, 1, 1, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 2, 1, 0, 1, 0, 2, 0, 1, 1, 2
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
f[p_, e_] := If[e == 1 && OddQ[PrimePi[p]], 1, 0]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 06 2023 *)
-
PARI
a(n) = {my(f = factor(n)); sum(i = 1, #f~, if(f[i,2] == 1 && primepi(f[i,1])%2, 1, 0));} \\ Amiram Eldar, Oct 06 2023
Formula
a(n) = Sum_{p|n, p prime} (pi(p) mod 2) * floor(1/gcd(p,n/p)).
From Amiram Eldar, Oct 06 2023: (Start)
Additive with a(p^e) = 1 if e = 1 and primepi(p) is odd and 0 otherwise. (End)