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A351230 Numerator of A003415(n) / A276086(n), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

%I A351230 #12 Feb 05 2022 17:05:53
%S A351230 0,0,1,1,4,1,1,1,4,1,7,1,16,1,3,4,32,1,21,1,8,1,13,1,44,1,1,9,32,1,31,
%T A351230 1,80,1,19,2,12,1,1,8,68,1,41,1,16,13,1,1,16,1,3,2,8,1,81,8,92,11,31,
%U A351230 1,92,1,11,17,64,1,61,1,24,13,59,1,156,1,13,11,16,1,71,1,176,18,43,1,124,11,3,16,4,1,123
%N A351230 Numerator of A003415(n) / A276086(n), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
%H A351230 Antti Karttunen, <a href="/A351230/b351230.txt">Table of n, a(n) for n = 0..65537</a>
%H A351230 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A351230 a(n) = A003415(n) / A327858(n) = A003415(n) / gcd(A003415(n), A276086(n)).
%o A351230 (PARI)
%o A351230 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351230 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A351230 A351230(n) = numerator(A003415(n) / A276086(n));
%Y A351230 Cf. A003415, A276086, A327858.
%Y A351230 Cf. A351231 (denominators), A351232.
%K A351230 nonn,frac,easy
%O A351230 0,5
%A A351230 _Antti Karttunen_, Feb 05 2022