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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
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OFFSET
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1,7
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COMMENTS
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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
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LINKS
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FORMULA
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Other identities. For all n >= 1:
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PROG
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(PARI)
for(n=1, 100, write("b265753.txt", n, " ", A265753(n)));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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