cp's OEIS Frontend

A347964 Greatest common divisor of A003415 (arithmetic derivative) and A003961 (prime shift towards larger primes).

%I A347964 #9 Dec 06 2021 11:01:57
%S A347964 1,1,1,1,1,5,1,3,1,7,1,1,1,3,1,1,1,3,1,3,5,13,1,1,1,3,1,1,1,1,1,1,1,
%T A347964 19,1,15,1,3,1,1,1,1,1,3,1,1,1,1,1,3,5,1,1,3,1,1,1,31,1,1,1,3,1,3,1,1,
%U A347964 1,9,1,1,1,3,1,3,5,1,1,1,1,1,1,43,1,1,1,3,1,1,1,3,1,3,1,1,1,1,1,11,25,7
%N A347964 Greatest common divisor of A003415 (arithmetic derivative) and A003961 (prime shift towards larger primes).
%H A347964 Antti Karttunen, <a href="/A347964/b347964.txt">Table of n, a(n) for n = 1..20000</a>
%H A347964 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A347964 a(n) = gcd(A003415(n), A003961(n)).
%F A347964 a(n) = gcd(A003415(n), A348937(n)) = gcd(A003961(n), A348937(n)). - _Antti Karttunen_, Dec 06 2021
%o A347964 (PARI)
%o A347964 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347964 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A347964 A347964(n) = gcd(A003415(n), A003961(n));
%Y A347964 Cf. also A085731, A322361, A347965, A348937.
%K A347964 nonn
%O A347964 1,6
%A A347964 _Antti Karttunen_, Sep 25 2021