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Denominator of n/A276086(A003415(n)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
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%I #11 Feb 11 2024 14:20:24

%S 1,1,1,2,9,2,3,2,25,5,1,2,75,2,15,1,21,2,125,2,125,15,25,2,175,9,75,

%T 1250,3,2,7,2,18375,25,125,5,49,2,375,75,147,2,15,2,875,14,625,2,

%U 128625,75,21,125,13125,2,6125,45,147,375,7,2,343,2,21,250,2941225,25,49,2,1225,625,1125,2,84035,2,105,350

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

%C Sequence contains only terms of A048103.

%H Antti Karttunen, <a href="/A370117/b370117.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A327859(n) / A369964(n) = A327859(n) / gcd(n, A276086(A003415(n))).

%F a(n) = A276086(A370120(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 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A370117(n) = { my(u=A276086(A003415(n))); (u/gcd(n, u)); };

%Y Cf. A003415, A276086, A327859, A369964, A370115 (positions of 1's), A370116 (numerators), A370120.

%K nonn,frac

%O 0,4

%A _Antti Karttunen_, Feb 11 2024