A343223 - OEIS

%I #9 May 23 2021 03:21:01

%S 1,1,1,1,1,5,1,12,2,1,1,4,1,3,1,1,1,1,1,3,1,1,1,4,2,15,1,32,1,1,1,1,1,

%T 1,1,4,1,3,1,1,1,1,1,16,13,5,1,16,1,1,5,1,1,1,1,4,1,1,1,4,1,3,1,3,1,1,

%U 1,1,1,1,1,1,1,3,1,16,3,1,1,1,1,1,1,4,1,3,1,4,1,3,1,48,1,1,1,8,1,1,1,2,1,1,1,1,1

%N a(n) = gcd(A003415(n), A003415(sigma(n))-n), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.

%H Antti Karttunen, <a href="/A343223/b343223.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = gcd(A003415(n), A342926(n)).

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A342926(n) = (A003415(sigma(n))-n);

%o A343223(n) = gcd(A003415(n), A342926(n));

%Y Cf. A000203, A003415, A342925, A342926.

%K nonn

%O 1,6

%A _Antti Karttunen_, Apr 15 2021