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Denominator of ratio A003415(n) / A003415(A276086(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
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%I #10 Jan 20 2024 18:37:36

%S 1,1,5,3,21,1,7,2,31,39,123,5,45,55,185,15,705,25,275,175,215,1425,

%T 3975,125,325,425,6125,4125,22125,1,9,1,41,51,55,1,59,71,247,159,951,

%U 95,365,115,1445,381,5385,325,2175,565,1655,2775,30075,1375,12625,8375,46625,63375,166125,7,77,91,329,35,427,119,483

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

%H Antti Karttunen, <a href="/A369039/b369039.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = A327860(n) / A345000(n) = A327860(n) / gcd(A003415(n), A327860(n)).

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o 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 A369039(n) = { my(u=A327860(n)); u/gcd(A003415(n),u); };

%Y Cf. A003415, A276086, A327860, A345000, A369038 (numerators).

%Y Cf. also A351231, A351251.

%K nonn,frac,easy

%O 1,3

%A _Antti Karttunen_, Jan 20 2024