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A246269 a(1) = 1, a(p(k)) = p(k+1) mod 4 for k-th prime p(k) and a(u * v) = a(u) * a(v) for u, v > 0.

%I A246269 #9 Sep 01 2014 11:45:46
%S A246269 1,3,1,9,3,3,3,27,1,9,1,9,1,9,3,81,3,3,3,27,3,3,1,27,9,3,1,27,3,9,1,
%T A246269 243,1,9,9,9,1,9,1,81,3,9,3,9,3,3,1,81,9,27,3,9,3,3,3,81,3,9,1,27,3,3,
%U A246269 3,729,3,3,3,27,1,27,1,27,3,3,9,27,3,3,3,243,1,9,1,27,9,9,3,27
%N A246269 a(1) = 1, a(p(k)) = p(k+1) mod 4 for k-th prime p(k) and a(u * v) = a(u) * a(v) for u, v > 0.
%C A246269 This is a fully multiplicative sequence. Only powers of 3 (A000244) occur as terms.
%H A246269 Antti Karttunen, <a href="/A246269/b246269.txt">Table of n, a(n) for n = 1..10080</a>
%F A246269 a(n) = A065338(A003961(n)).
%F A246269 a(n) = A000244(A246270(n)).
%e A246269 For n = 10 = 2*5 = p_1 * p_3 we have a(n) = (p_{1+1} mod 4)*(p_{3+1} mod 4) = (p_2 mod 4) * (p_4 mod 4) = (3 mod 4)*(7 mod 4) = 3*3 = 9.
%o A246269 (PARI)
%o A246269 default(primelimit, 2^22)
%o A246269 A246269(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = (nextprime(f[i, 1]+1)%4)); factorback(f);
%o A246269 for(n=1, 10080, write("b246269.txt", n, " ", A246269(n)));
%o A246269 (Scheme) (define (A246269 n) (A065338 (A003961 n)))
%Y A246269 Cf. A000244, A003961, A065338, A246270, A246272.
%K A246269 nonn,mult
%O A246269 1,2
%A A246269 _Antti Karttunen_, Aug 21 2014