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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Aug 21 2014

Keywords

• nonn
• mult

Comments

This is a fully multiplicative sequence. Only powers of 3 (A000244) occur as terms.

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10080

Crossrefs

Cf. A000244, A003961, A065338, A246270, A246272.

Programs

PARI

default(primelimit, 2^22)
A246269(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = (nextprime(f[i, 1]+1)%4)); factorback(f);
for(n=1, 10080, write("b246269.txt", n, " ", A246269(n)));

Scheme

(define (A246269 n) (A065338 (A003961 n)))

Formula

a(n) = A065338(A003961(n)).

a(n) = A000244(A246270(n)).