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A343223 a(n) = gcd(A003415(n), A003415(sigma(n))-n), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.

%I A343223 #9 May 23 2021 03:21:01
%S A343223 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 A343223 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 A343223 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 A343223 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 A343223 Antti Karttunen, <a href="/A343223/b343223.txt">Table of n, a(n) for n = 1..65537</a>
%H A343223 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A343223 a(n) = gcd(A003415(n), A342926(n)).
%o A343223 (PARI)
%o A343223 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A343223 A342926(n) = (A003415(sigma(n))-n);
%o A343223 A343223(n) = gcd(A003415(n), A342926(n));
%Y A343223 Cf. A000203, A003415, A342925, A342926.
%K A343223 nonn
%O A343223 1,6
%A A343223 _Antti Karttunen_, Apr 15 2021