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A370130 a(n) = A369669(A276086(n)), where A369669 is the greatest common divisor of the first and second arithmetic derivative of n, and A276086 is the primorial base exp-function.

%I A370130 #16 Feb 13 2024 14:34:07
%S A370130 0,1,1,1,1,1,1,1,4,1,1,1,1,3,1,1,16,1,5,5,5,5,5,5,100,25,25,175,25,25,
%T A370130 1,3,1,1,1,1,4,1,1,1,1,1,1,1,4,17,1,1,5,5,5,5,20,5,25,25,25,25,325,25,
%U A370130 1,1,1,1,4,1,1,1,1,1,11,1,4,1,1,1,1,1,5,5,320,95,5,5,25,25,25,25,100,25,7,7,112,7,7,7,7,7,7,7,28
%N A370130 a(n) = A369669(A276086(n)), where A369669 is the greatest common divisor of the first and second arithmetic derivative of n, and A276086 is the primorial base exp-function.
%H A370130 Antti Karttunen, <a href="/A370130/b370130.txt">Table of n, a(n) for n = 0..16384</a>
%H A370130 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A370130 a(n) = A369669(A276086(n)).
%F A370130 a(n) = gcd(A327860(n), A370131(n)).
%F A370130 For n >= 1, a(n) = A085731(A327860(n)).
%o A370130 (PARI)
%o A370130 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A370130 A369669(n) = { my(d=A003415(n)); gcd(d, A003415(d)); };
%o A370130 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A370130 A370130(n) = A369669(A276086(n));
%Y A370130 Cf. A003415, A068346, A085731, A276086, A327860, A328242 (positions of 1's), A370131.
%Y A370130 Cf. A000012, A024451, A143293.
%K A370130 nonn,look
%O A370130 0,9
%A A370130 _Antti Karttunen_, Feb 10 2024