A369967 a(n) = 1 if the arithmetic derivative of n is a multiple of 5, otherwise 0.

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

Offset

0

Comments

Question: Is the asymptotic mean of this sequence 1/5? See also conjecture in A369968.

Links

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

Index entries for characteristic functions

Formula

a(n) >= A369968(n).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369967(n) = (0==(A003415(n)%5));

Crossrefs

Characteristic function of A327865.

Cf. A003415, A369968.

Cf. also A358680, A359430, A353494, A370118, for cases k = 2, 3, 4, 9 of characteristic functions for numbers whose arithmetic derivative is multiple of k.

Sequence in context: A016338 A266253 A113052 * A256432 A218171 A362130

Adjacent sequences: A369964 A369965 A369966 * A369968 A369969 A369970

Keyword

nonn,changed

Author

Antti Karttunen, Feb 10 2024

Status

approved