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A345375
Number of unitary prime divisors of n whose prime index is even.
2
0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 2, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 2, 0, 1, 2, 0, 1, 0, 2, 0, 1
OFFSET
1,21
LINKS
FORMULA
a(n) = Sum_{p|n, p prime} ((pi(p)+1) mod 2) * floor(1/gcd(p,n/p)).
From Amiram Eldar, Oct 06 2023: (Start)
a(n) = A056169(n) - A345374(n).
a(n) <= A324967(n), with equality if and only if n is squarefree (A005117).
Additive with a(p^e) = 1 if e = 1 and primepi(p) is even and 0 otherwise. (End)
MATHEMATICA
f[p_, e_] := If[e == 1 && EvenQ[PrimePi[p]], 1, 0]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 06 2023 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jun 16 2021
STATUS
approved