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A368647
The number of distinct primes of the form 3*k+2 dividing n minus the number of distinct primes of the form 3*k+1 dividing n.
1
0, 1, 0, 1, 1, 1, -1, 1, 0, 2, 1, 1, -1, 0, 1, 1, 1, 1, -1, 2, -1, 2, 1, 1, 1, 0, 0, 0, 1, 2, -1, 1, 1, 2, 0, 1, -1, 0, -1, 2, 1, 0, -1, 2, 1, 2, 1, 1, -1, 2, 1, 0, 1, 1, 2, 0, -1, 2, 1, 2, -1, 0, -1, 1, 0, 2, -1, 2, 1, 1, 1, 1, -1, 0, 1, 0, 0, 0, -1, 2, 0, 2
OFFSET
1,10
LINKS
FORMULA
Additive with a(p^e) = 0 if p = 3, 1 if p == 2 (mod 3), and -1 if p == 1 (mod 3).
a(n) = A005090(n) - A005088(n).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A086241 = 0.641944... .
MATHEMATICA
f[p_, e_] := Switch[Mod[p, 3], 0, 0, 1, -1, 2, 1]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(p = factor(n)[, 1]); sum(i = 1, #p, if(p[i]%3 == 0, 0, if(p[i]%3 == 1, -1, 1))); }
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Amiram Eldar, Jan 02 2024
STATUS
approved