A265753 - OEIS

A265753

a(n) = A007949(A265399(n)).

0, 0, 1, 0, 1, 1, 2, 0, 2, 1, 3, 1, 5, 2, 2, 0, 8, 2, 13, 1, 3, 3, 21, 1, 2, 5, 3, 2, 34, 2, 55, 0, 4, 8, 3, 2, 89, 13, 6, 1, 144, 3, 233, 3, 3, 21, 377, 1, 4, 2, 9, 5, 610, 3, 4, 2, 14, 34, 987, 2, 1597, 55, 4, 0, 6, 4, 2584, 8, 22, 3, 4181, 2, 6765, 89, 3, 13, 5, 6, 10946, 1, 4, 144, 17711, 3, 9, 233, 35, 3, 28657, 3, 7, 21

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,7

COMMENTS

a(n) = Coefficient of x in the reduction under x^2->x+1 of the polynomial encoded in the prime factorization of n. (Assuming here only polynomials with nonnegative integer coefficients, see e.g. A206296 for the details).

Completely additive with a(prime(k)) = F(k-1), where F(k) denotes the k-th Fibonacci number, A000045(k). - Peter Munn, Mar 29 2021, incorporating comment by Antti Karttunen, Dec 15 2015

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100

FORMULA

a(n) = A007949(A265399(n)).

Other identities. For all n >= 1:

a(A000040(n)) = A000045(n-1). [Generalized by Peter Munn, Mar 29 2021]

a(A206296(n)) = A112576(n).

a(A265750(n)) = A192751(n).

PROG

(PARI)

\\ Needs also code from A265398 and A265399.

A265753 = n -> valuation(A265399(n), 3);