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A351231 Denominator of A003415(n) / A276086(n), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

%I A351231 #16 Feb 05 2022 17:06:08
%S A351231 1,1,3,6,9,18,1,10,5,5,45,90,25,50,25,75,225,450,125,250,125,75,1125,
%T A351231 2250,625,125,125,1250,5625,11250,7,14,21,3,63,21,7,70,5,105,315,630,
%U A351231 175,350,175,350,63,3150,125,125,175,525,1125,15750,4375,4375,13125,13125,39375,78750,49,98,49,98,147,49,245,490,245
%N A351231 Denominator of A003415(n) / A276086(n), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
%H A351231 Antti Karttunen, <a href="/A351231/b351231.txt">Table of n, a(n) for n = 0..11550</a>
%H A351231 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A351231 a(n) = A276086(n) / A327858(n) = A276086(n) / gcd(A003415(n), A276086(n)).
%F A351231 a(n) = A276086(A351233(n)).
%o A351231 (PARI)
%o A351231 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351231 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A351231 A351231(n) = denominator(A003415(n) / A276086(n));
%Y A351231 Cf. A003415, A276086, A327858, A351230 (numerators), A351232, A351233.
%K A351231 nonn,base,easy,frac,look
%O A351231 0,3
%A A351231 _Antti Karttunen_, Feb 05 2022