cp's OEIS Frontend

A369038 Numerator of ratio A003415(n) / A003415(A276086(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

%I A369038 #10 Jan 20 2024 18:37:31
%S A369038 0,1,1,2,1,5,1,3,6,7,1,8,1,9,8,2,1,7,1,12,2,13,1,11,2,3,27,16,1,31,1,
%T A369038 8,14,19,4,5,1,21,16,34,1,41,1,12,39,5,1,56,14,9,4,14,1,27,16,46,22,
%U A369038 31,1,46,1,33,51,16,6,61,1,36,26,59,1,13,1,39,1,8,6,71,1,11,108,43,1,62,22,9,32,1,1,41,20
%N A369038 Numerator of ratio A003415(n) / A003415(A276086(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
%H A369038 Antti Karttunen, <a href="/A369038/b369038.txt">Table of n, a(n) for n = 1..16384</a>
%F A369038 a(n) = A003415(n) / A345000(n) = A003415(n) / gcd(A003415(n), A327860(n)).
%o A369038 (PARI)
%o A369038 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369038 A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
%o A369038 A369038(n) = { my(u=A003415(n)); (u/gcd(u,A327860(n))); };
%Y A369038 Cf. A003415, A276086, A327860, A345000, A369039 (denominators).
%Y A369038 Cf. also A351230, A351250.
%K A369038 nonn,frac,easy
%O A369038 1,4
%A A369038 _Antti Karttunen_, Jan 20 2024