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A343226 a(n) = gcd(sigma(n), n+A003415(n)), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.

%I A343226 #15 Jun 02 2021 22:43:09
%S A343226 1,3,4,1,6,1,8,5,1,1,12,28,14,1,1,1,18,39,20,2,1,1,24,4,1,1,2,4,30,1,
%T A343226 32,7,1,1,1,1,38,1,1,18,42,1,44,4,6,1,48,4,3,1,1,2,54,15,1,4,1,1,60,8,
%U A343226 62,1,2,1,1,1,68,14,1,3,72,3,74,1,2,4,1,1,80,2,1,1,84,16,1,1,1,12,90,3,1,4,1,1,1,4
%N A343226 a(n) = gcd(sigma(n), n+A003415(n)), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
%C A343226 a(n) = n+1 iff n is prime (A000040). - _Bernard Schott_, Jun 01 2021
%H A343226 Antti Karttunen, <a href="/A343226/b343226.txt">Table of n, a(n) for n = 1..20000</a>
%H A343226 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A343226 a(n) = gcd(A000203(n), A129283(n)) = gcd(A000203(n), A211991(n)).
%F A343226 a(n) = A000203(n) / A343227(n).
%F A343226 a(n) = 1 if n is squarefree semiprime (A006881). - _Bernard Schott_, Jun 02 2021
%o A343226 (PARI)
%o A343226 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A343226 A129283(n) = (n+A003415(n));
%o A343226 A343226(n) = gcd(sigma(n), A129283(n));
%Y A343226 Cf. A000203, A003415, A129283, A211991, A343227.
%K A343226 nonn
%O A343226 1,2
%A A343226 _Antti Karttunen_, Apr 15 2021