cp's OEIS Frontend

A373145 a(n) = gcd(A003415(n), A276085(n)), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

%I A373145 #12 Jun 03 2024 16:56:16
%S A373145 0,1,1,2,1,1,1,3,2,7,1,4,1,1,8,4,1,1,1,8,2,1,1,1,2,1,3,32,1,1,1,5,2,1,
%T A373145 12,6,1,1,8,1,1,1,1,4,1,1,1,2,2,1,4,8,1,1,8,1,2,1,1,2,1,1,17,6,6,1,1,
%U A373145 8,2,1,1,1,1,1,1,16,6,1,1,2,4,1,1,2,2,1,8,1,1,1,20,4,2,1,12,1,1,1,1,14,1,1,1,1,1
%N A373145 a(n) = gcd(A003415(n), A276085(n)), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.
%H A373145 Antti Karttunen, <a href="/A373145/b373145.txt">Table of n, a(n) for n = 1..65537</a>
%F A373145 a(n) = gcd(A003415(n), A373146(n)) = gcd(A276085(n), A373146(n)).
%F A373145 For n > 1, a(n) = gcd(A276085(n), A373147(n)) = gcd(A003415(n), A373148(n)).
%o A373145 (PARI)
%o A373145 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A373145 A002110(n) = prod(i=1,n,prime(i));
%o A373145 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%o A373145 A373145(n) = gcd(A003415(n), A276085(n));
%Y A373145 Cf. A003415, A276086, A373146, A373147, A373148.
%Y A373145 Cf. A368998 (positions of even terms), A368999 (of odd terms), A373144 (of multiples of 3).
%Y A373145 Cf. also A327858.
%K A373145 nonn
%O A373145 1,4
%A A373145 _Antti Karttunen_, May 26 2024