A374110 a(n) = 1 if A113177(n) and A328845(n) are both multiples of 3, otherwise 0, where A113177 is fully additive with a(p) = Fibonacci(p) and A328845 is the first Fibonacci-based variant of the arithmetic derivative.

1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Formula

a(n) = A374051(n) * A374121(n).

a(n) = A079978(A374106(n)).

Prog

(PARI)
A113177(n) = if(n<=1, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2]*fibonacci(f[i, 1])));
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]));
A374110(n) = (!(A113177(n)%3) && !(A328845(n)%3));

Crossrefs

Characteristic function of A374111.

Cf. A000045, A079978, A113177, A328845, A374051, A374106, A374121.

Sequence in context: A205808 A238897 A373975 * A297199 A373477 A185117

Adjacent sequences: A374107 A374108 A374109 * A374111 A374112 A374113

Keyword

nonn

Author

Antti Karttunen, Jun 29 2024

Status

approved