login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A278509
a(n) = 3^{number of primes congruent to 3 modulo 4 dividing n (with multiplicity)}.
3
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
OFFSET
1,3
LINKS
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
(Scheme) (define (A278509 n) (A065338 (A000265 n)))
CROSSREFS
Cf. also A278265.
Sequence in context: A336456 A227898 A035649 * A094782 A035666 A060592
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Nov 28 2016
STATUS
approved