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A369967 a(n) = 1 if the arithmetic derivative of n is a multiple of 5, otherwise 0. 2
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 (list; graph; refs; listen; history; text; internal format)
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
AUTHOR
Antti Karttunen, Feb 10 2024
STATUS
approved

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Last modified August 29 15:03 EDT 2024. Contains 375517 sequences. (Running on oeis4.)