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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A373256 a(n) = 1 if A003415(n) == -1 (mod 3), otherwise 0, where A003415 is the arithmetic derivative. 4 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 (list; graph; refs; listen; history; text; internal format) OFFSET 0 COMMENTS Question: Do the asymptotic means of this sequence, A373254 and A359430 all converge to 1/3, or do they differ or diverge? LINKS Antti Karttunen, Table of n, a(n) for n = 0..100000 Index entries for characteristic functions FORMULA a(n) = [A373253(n) == -1], where [ ] is the Iverson bracket. a(n) = 1 - (A359430(n)+A373254(n)). PROG (PARI) A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1])); A373256(n) = (2==(A003415(n)%3)); CROSSREFS Characteristic function of A373257. Cf. A003415, A359430, A373253, A373254. Sequence in context: A358842 A358758 A185708 * A286996 A044937 A025459 Adjacent sequences: A373253 A373254 A373255 * A373257 A373258 A373259 KEYWORD nonn AUTHOR Antti Karttunen, Jun 01 2024 STATUS approved

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