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A358229 Numbers k such that A276086(k) mod A003415(k) is an even number, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

%I A358229 #6 Nov 25 2022 11:10:49
%S A358229 2,3,5,6,7,9,11,13,15,17,18,19,21,23,25,26,27,29,31,33,34,35,37,38,39,
%T A358229 41,43,45,46,47,49,51,53,55,57,59,61,65,67,69,70,71,73,77,79,81,82,83,
%U A358229 85,86,87,89,91,93,94,95,97,101,103,105,106,107,109,111,113,115,117,118,119,121,123,125,127,129,130,131
%N A358229 Numbers k such that A276086(k) mod A003415(k) is an even number, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
%H A358229 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A358229 (PARI)
%o A358229 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A358229 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A358229 A358227(n) = ((A276086(n)%A003415(n))%2);
%o A358229 isA358229(n) = !A358227(n);
%Y A358229 Complement: {1} U A358228.
%Y A358229 Cf. A003415, A276086, A328382, A358221 (subsequence), A358227 (characteristic function).
%Y A358229 Cf. also A358226.
%K A358229 nonn
%O A358229 1,1
%A A358229 _Antti Karttunen_, Nov 25 2022