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A369968 a(n) = 1 if n is not multiple of 5, but its arithmetic derivative is, otherwise 0. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 29 13:35 EDT 2024. Contains 375517 sequences. (Running on oeis4.)