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A370116 Numerator of n/A276086(A003415(n)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

%I A370116 #7 Feb 11 2024 14:20:17
%S A370116 0,1,1,3,4,5,1,7,8,9,1,11,4,13,7,1,16,17,3,19,4,7,11,23,8,5,13,9,4,29,
%T A370116 15,31,32,11,17,7,36,37,19,13,8,41,1,43,44,3,23,47,16,49,1,17,52,53,9,
%U A370116 11,8,19,29,59,20,61,31,3,64,13,33,67,68,23,1,71,72,73,37,3,76,77,13,79,16,81,41,83,4,17,43
%N A370116 Numerator of n/A276086(A003415(n)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
%H A370116 Antti Karttunen, <a href="/A370116/b370116.txt">Table of n, a(n) for n = 0..16384</a>
%F A370116 a(n) = n / A369964(n) = n / gcd(n, A276086(A003415(n))).
%o A370116 (PARI)
%o A370116 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A370116 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A370116 A370116(n) = (n/gcd(n, A276086(A003415(n))));
%Y A370116 Cf. A003415, A276086, A327859, A369964, A370114 (positions of 1's), A370117 (denominators).
%K A370116 nonn,frac
%O A370116 0,4
%A A370116 _Antti Karttunen_, Feb 11 2024