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A358221 Numbers k such that A003415(k) divides A276086(k), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

%I A358221 #17 Feb 22 2024 20:08:36
%S A358221 2,3,5,6,7,9,11,13,17,19,21,23,25,26,29,31,33,37,38,41,43,46,47,49,53,
%T A358221 59,61,65,67,71,73,77,79,83,89,94,97,101,103,107,109,113,127,131,137,
%U A358221 139,141,146,149,151,157,161,163,167,173,179,181,185,191,193,197,199,201,206,207,209,211,221,223,227,229,233
%N A358221 Numbers k such that A003415(k) divides A276086(k), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
%H A358221 Antti Karttunen, <a href="/A358221/b358221.txt">Table of n, a(n) for n = 1..10000</a>
%o A358221 (PARI)
%o A358221 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A358221 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A358221 A358220(n) = if(n<2,0,!(A276086(n)%A003415(n)));
%o A358221 isA358221(n) = A358220(n);
%Y A358221 Union of A000040 and A358222.
%Y A358221 Subsequence of A358215 (thus also of A048103) and of A358229.
%Y A358221 Positions of zeros in A328382.
%Y A358221 Cf. A003415, A276086, A358220 (characteristic function).
%Y A358221 Cf. also A328387, A356311, A356312.
%K A358221 nonn
%O A358221 1,1
%A A358221 _Antti Karttunen_, Nov 23 2022