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%I A373256 #9 Jun 01 2024 08:14:52
%S A373256 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,
%T A373256 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,
%U A373256 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
%N A373256 a(n) = 1 if A003415(n) == -1 (mod 3), otherwise 0, where A003415 is the arithmetic derivative.
%C A373256 Question: Do the asymptotic means of this sequence, A373254 and A359430 all converge to 1/3, or do they differ or diverge?
%H A373256 Antti Karttunen, <a href="/A373256/b373256.txt">Table of n, a(n) for n = 0..100000</a>
%H A373256 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F A373256 a(n) = [A373253(n) == -1], where [ ] is the Iverson bracket.
%F A373256 a(n) = 1 - (A359430(n)+A373254(n)).
%o A373256 (PARI)
%o A373256 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A373256 A373256(n) = (2==(A003415(n)%3));
%Y A373256 Characteristic function of A373257.
%Y A373256 Cf. A003415, A359430, A373253, A373254.
%K A373256 nonn
%O A373256 0
%A A373256 _Antti Karttunen_, Jun 01 2024

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