A278509 - OEIS

A278509

a(n) = 3^{number of primes congruent to 3 modulo 4 dividing n (with multiplicity)}.

1, 1, 3, 1, 1, 3, 3, 1, 9, 1, 3, 3, 1, 3, 3, 1, 1, 9, 3, 1, 9, 3, 3, 3, 1, 1, 27, 3, 1, 3, 3, 1, 9, 1, 3, 9, 1, 3, 3, 1, 1, 9, 3, 3, 9, 3, 3, 3, 9, 1, 3, 1, 1, 27, 3, 3, 9, 1, 3, 3, 1, 3, 27, 1, 1, 9, 3, 1, 9, 3, 3, 9, 1, 1, 3, 3, 9, 3, 3, 1, 81, 1, 3, 9, 1, 3, 3, 3, 1, 9, 3, 3, 9, 3, 3, 3, 1, 9, 27, 1, 1, 3, 3, 1, 9, 1, 3, 27, 1, 3, 3, 3, 1, 9, 3, 1, 9, 3, 3, 3

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OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

Fully multiplicative with a(p^e) = 1 if p = 2, (p mod 4)^e if p > 2.

a(n) = A065338(A000265(n)) = A000265(A065338(n)).

a(n) = A000244(A065339(n)) = 3^A065339(n).

MATHEMATICA

f[p_, e_] := Mod[p, 4]^e; f[2, e_] := 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 13 2023 *)

PROG