%I #21 Apr 05 2021 04:00:29

%S 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,

%T 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,

%U 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

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

%C 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).

%C 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

%H Antti Karttunen, <a href="/A265753/b265753.txt">Table of n, a(n) for n = 1..100</a>

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

%F Other identities. For all n >= 1:

%F a(A000040(n)) = A000045(n-1). [Generalized by _Peter Munn_, Mar 29 2021]

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

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

%o (PARI)

%o \\ Needs also code from A265398 and A265399.

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

%o for(n=1, 100, write("b265753.txt", n, " ", A265753(n)));

%o (Scheme) (define (A265753 n) (A007949 (A265399 n)))

%Y Cf. A007949, A112576, A192751, A206296, A265399, A265750, A265752.

%Y Cf. also A000040, A000045.

%K nonn

%O 1,7

%A _Antti Karttunen_, Dec 15 2015