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A374036
a(n) = 1 if A328845(n) and A328846(n) are both even, otherwise 0, where A328845 and A328846 are the first and second Fibonacci-based variants of the arithmetic derivative.
4
1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1
OFFSET
0
FORMULA
a(n) = A374045(n) * A374048(n).
a(n) = A059841(A374035(n)).
PROG
(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]));
A374036(n) = (!(A328845(n)%2) && !(A328846(n)%2));
CROSSREFS
Characteristic function of A374037, whose complement A374038 gives the indices of 0's.
Sequence in context: A353494 A190610 A095901 * A087049 A358680 A186447
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 28 2024
STATUS
approved