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A374035
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a(n) = gcd(A328845(n), A328846(n)), where A328845 and A328846 are the first and second Fibonacci-based variants of the arithmetic derivative.
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6
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0, 0, 1, 1, 4, 5, 1, 1, 12, 6, 5, 1, 4, 1, 3, 5, 32, 1, 3, 1, 20, 1, 3, 1, 4, 50, 1, 27, 8, 1, 5, 1, 80, 1, 1, 25, 12, 1, 1, 1, 20, 1, 1, 1, 20, 15, 7, 1, 16, 14, 25, 1, 4, 1, 27, 20, 4, 1, 1, 1, 80, 1, 33, 3, 192, 10, 1, 1, 8, 1, 5, 1, 12, 1, 1, 25, 12, 1, 1, 1, 80, 108, 1, 1, 4, 15, 1, 1, 4, 1, 15, 1, 60, 1, 1, 10, 16
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OFFSET
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0,5
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LINKS
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FORMULA
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For all n>= 0, a(5*n) == 0 (mod 5). [There are multiples of 5 at other positions also]
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PROG
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(PARI)
A328845(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(f[i, 1])/f[i, 1]));
A328846(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(2+primepi(f[i, 1]))/f[i, 1]));
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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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