A369968 a(n) = 1 if n is not multiple of 5, but its arithmetic derivative is, otherwise 0.

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

Offset

0

Comments

Conjecture: the asymptotic mean of this sequence is (4/5)*(1/5) = 4/25 = 0.16. Compare to A369967 and the conjecture at A369658.

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Index entries for characteristic functions

Formula

a(n) = A011558(n) * A369967(n).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369968(n) = ((n%5)&&(0==(A003415(n)%5)));

Crossrefs

Characteristic function of A369969.

Cf. A003415, A011558, A369967.

Cf. also A353557, A369658, A360109, for cases k = 2, 3, 4 of the characteristic functions for nonmultiples of k whose arithmetic derivative is multiple of k.

Sequence in context: A228495 A356982 A284683 * A288673 A030213 A187969

Adjacent sequences: A369965 A369966 A369967 * A369969 A369970 A369971

Keyword

nonn

Author

Antti Karttunen, Feb 10 2024

Status

approved