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A369964 a(n) = gcd(n, A276086(A003415(n))), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

%I A369964 #9 Feb 11 2024 14:19:54
%S A369964 1,1,2,1,1,1,6,1,1,1,10,1,3,1,2,15,1,1,6,1,5,3,2,1,3,5,2,3,7,1,2,1,1,
%T A369964 3,2,5,1,1,2,3,5,1,42,1,1,15,2,1,3,1,50,3,1,1,6,5,7,3,2,1,3,1,2,21,1,
%U A369964 5,2,1,1,3,70,1,1,1,2,25,1,1,6,1,5,1,2,1,21,5,2,3,1,1,6,1,1,3,2,5,3,1,98,3,25
%N A369964 a(n) = gcd(n, A276086(A003415(n))), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
%H A369964 Antti Karttunen, <a href="/A369964/b369964.txt">Table of n, a(n) for n = 0..65537</a>
%F A369964 a(n) = gcd(n, A327859(n)) = gcd(n, A276086(A003415(n))).
%F A369964 For n >= 1, a(n) = n / A370116(n).
%F A369964 For n >= 0, a(n) = A327859(n) / A370117(n).
%o A369964 (PARI)
%o A369964 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369964 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A369964 A369964(n) = gcd(n, A276086(A003415(n)));
%Y A369964 Cf. A003415, A276086, A327859, A370114 (fixed points, see also A369650), A370116, A370117.
%K A369964 nonn
%O A369964 0,3
%A A369964 _Antti Karttunen_, Feb 11 2024