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%I #11 Nov 04 2022 11:26:08
%S 2,1,1,1,1,5,1,3,2,1,1,1,1,3,2,1,1,1,1,3,10,1,1,1,2,15,3,1,1,1,1,1,14,
%T 1,6,5,1,21,2,1,1,1,1,3,1,25,1,7,2,3,10,7,1,1,2,1,2,1,1,1,1,3,1,3,18,
%U 1,1,3,2,1,1,1,1,3,1,5,18,1,1,1,2,1,1,1,2,15,2,35,1,1,2,3,2,49,6,1,1,1,5,7,1,7,1,1,1
%N a(n) = gcd(A276086(n), A342001(n)), where A276086 is the primorial base exp-function, and A342001 is the arithmetic derivative without its inherited divisor.
%C Each term a(n) is a factor of A327858(n).
%H Antti Karttunen, <a href="/A356299/b356299.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%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 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A342001(n) = (A003415(n) / A003557(n));
%o A356299(n) = gcd(A276086(n), A342001(n));
%Y Cf. A003415, A003557, A046337 (positions of even terms), A276086, A342001, A327858.
%K nonn
%O 1,1
%A _Antti Karttunen_, Nov 03 2022
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