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%I #6 Nov 06 2021 20:14:52
%S 1,3,4,7,6,3,8,15,13,1,12,1,14,1,1,31,18,3,20,3,1,1,24,3,31,1,40,7,30,
%T 3,32,63,1,1,1,1,38,1,1,5,42,3,44,3,2,1,48,1,57,3,1,1,54,3,1,1,1,1,60,
%U 1,62,1,4,127,1,3,68,3,1,1,72,3,74,1,2,1,1,3,80,3,121,1,84,1,1,1,1,1,90,117,1,3,1,1,1,3
%N a(n) = gcd(sigma(n), A332994(n)).
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = gcd(A000203(n), A332994(n)).
%F a(n) = gcd(A000203(n), A333784(n)) = gcd(A332994(n), A333784(n)).
%F a(n) = A332994(n) / A348988(n) = A000203(n) / A348989(n).
%t f[n_] := n/FactorInteger[n][[-1, 1]]; g[1] = 1; g[n_] := g[n] = n + g[f[n]]; a[n_] := GCD[g[n], DivisorSigma[1, n]]; Array[a, 100] (* _Amiram Eldar_, Nov 06 2021 *)
%o (PARI)
%o A332994(n) = if(1==n,n,n + A332994(n/vecmax(factor(n)[,1])));
%o A348987(n) = gcd(sigma(n), A332994(n));
%Y Cf. A000203, A332994, A333784, A348988, A348989.
%Y Cf. also A348977.
%K nonn
%O 1,2
%A _Antti Karttunen_, Nov 06 2021
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