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%I #20 Apr 10 2021 22:27:21
%S 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,
%T 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,
%U 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
%N a(n) = A007814(A265399(n)).
%C 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).
%C 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
%H Antti Karttunen, <a href="/A265752/b265752.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = A007814(A265399(n)).
%F Other identities. For all n >= 1:
%F a(A000040(n+1)) = A000045(n-1). [Generalized by _Peter Munn_, Apr 05 2021]
%F a(A206296(n)) = A192232(n).
%F a(A265750(n)) = A192750(n).
%o (PARI)
%o \\ Needs also code from A265398 and A265399.
%o A265752 = n -> valuation(A265399(n),2);
%o for(n=1, 100, write("b265752.txt", n, " ", A265752(n)));
%o (Scheme) (define (A265752 n) (A007814 (A265399 n)))
%Y Cf. A007814, A192232, A192750, A206296, A265399, A265750, A265753.
%Y Cf. also A000040, A000045/A039834.
%K nonn
%O 1,4
%A _Antti Karttunen_, Dec 15 2015
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