A265752 a(n) = A007814(A265399(n)).

0, 1, 0, 2, 1, 1, 1, 3, 0, 2, 2, 2, 3, 2, 1, 4, 5, 1, 8, 3, 1, 3, 13, 3, 2, 4, 0, 3, 21, 2, 34, 5, 2, 6, 2, 2, 55, 9, 3, 4, 89, 2, 144, 4, 1, 14, 233, 4, 2, 3, 5, 5, 377, 1, 3, 4, 8, 22, 610, 3, 987, 35, 1, 6, 4, 3, 1597, 7, 13, 3, 2584, 3, 4181, 56, 2, 10, 3, 4, 6765, 5, 0, 90, 10946, 3, 6, 145, 21, 5, 17711

Offset

1,4

Comments

a(n) is the constant term of the reduction by 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 of the encoding).

Completely additive with a(prime(k)) = F(k-2), where F(k) denotes the k-th Fibonacci number, A000045(k) for k >= 0, or A039834(-k) for k <= 0. - Peter Munn, Apr 05 2021, incorporating comment by Antti Karttunen, Dec 15 2015

Links

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

Formula

a(n) = A007814(A265399(n)).

Other identities. For all n >= 1:

a(A000040(n+1)) = A000045(n-1). [Generalized by Peter Munn, Apr 05 2021]

a(A206296(n)) = A192232(n).

a(A265750(n)) = A192750(n).

Prog

(PARI)
\\ Needs also code from A265398 and A265399.
A265752 = n -> valuation(A265399(n), 2);
for(n=1, 100, write("b265752.txt", n, " ", A265752(n)));
(Scheme) (define (A265752 n) (A007814 (A265399 n)))

Crossrefs

Cf. A007814, A192232, A192750, A206296, A265399, A265750, A265753.

Cf. also A000040, A000045/A039834.

Sequence in context: A323618 A364650 A246270 * A125090 A294880 A212219

Adjacent sequences: A265749 A265750 A265751 * A265753 A265754 A265755

Keyword

nonn

Author

Antti Karttunen, Dec 15 2015

Status

approved