%I #5 Jun 26 2024 19:47:22

%S 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 12,1,6,4,223092870,1,6469693230,5,4,1,12,6,200560490130,1,4,9,

%U 7420738134810,1,304250263527210,4,2,1,13082761331670030,2,60,1,4,4,614889782588491410,1,36,3,16,1,32589158477190044730,2

%N 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 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%o (PARI)

%o A002110(n) = prod(i=1,n,prime(i));

%o A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };

%o 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(n) = gcd(A276085(n), A328768(n));

%Y Cf. A002110, A276085, A328768, A374042 (positions of multiples of 3).

%K nonn

%O 1,3

%A _Antti Karttunen_, Jun 26 2024