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A374031 a(n) = gcd(A276085(n), A328768(n)), where A276085 is the primorial base log-function, and A328768 is the first primorial based variant of arithmetic derivative.

%I A374031 #5 Jun 26 2024 19:47:22
%S A374031 0,1,2,2,6,1,30,3,4,1,210,4,2310,1,4,4,30030,1,510510,4,8,1,9699690,1,
%T A374031 12,1,6,4,223092870,1,6469693230,5,4,1,12,6,200560490130,1,4,9,
%U A374031 7420738134810,1,304250263527210,4,2,1,13082761331670030,2,60,1,4,4,614889782588491410,1,36,3,16,1,32589158477190044730,2
%N A374031 a(n) = gcd(A276085(n), A328768(n)), where A276085 is the primorial base log-function, and A328768 is the first primorial based variant of arithmetic derivative.
%H A374031 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A374031 (PARI)
%o A374031 A002110(n) = prod(i=1,n,prime(i));
%o A374031 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%o A374031 A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1])-1)/f[i, 1]));
%o A374031 A374031(n) = gcd(A276085(n), A328768(n));
%Y A374031 Cf. A002110, A276085, A328768, A374042 (positions of multiples of 3).
%K A374031 nonn
%O A374031 1,3
%A A374031 _Antti Karttunen_, Jun 26 2024