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A324058 a(n) = A324121(A005940(1+n)) = gcd(A324054(n), A005940(1+n)*A106737(n)).

%I A324058 #6 Feb 16 2019 20:38:44
%S A324058 1,1,2,1,2,12,1,1,2,2,12,4,1,3,4,1,2,8,4,6,4,24,6,12,3,3,2,1,4,24,1,3,
%T A324058 2,4,12,56,4,48,2,10,4,16,24,24,2,18,120,4,1,3,6,1,6,12,1,3,4,4,24,8,
%U A324058 1,3,2,1,2,2,4,12,4,48,6,8,28,8,24,112,6,24,8,2,4,16,24,336,8,96,12,120,6,24,4,6,8,720,6,36,3,3,2,21,6,36,3,15,14,6
%N A324058 a(n) = A324121(A005940(1+n)) = gcd(A324054(n), A005940(1+n)*A106737(n)).
%H A324058 Antti Karttunen, <a href="/A324058/b324058.txt">Table of n, a(n) for n = 0..16384</a>
%H A324058 Antti Karttunen, <a href="/A324058/a324058.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%F A324058 a(n) = A324121(A005940(1+n)) = gcd(A324054(n), A005940(1+n)*A106737(n)).
%o A324058 (PARI)
%o A324058 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A324058 A106737(n) = sum(k=0, n, (binomial(n+k, n-k)*binomial(n, k)) % 2);
%o A324058 A324054(n) = { my(p=2,mp=p*p,m=1); while(n, if(!(n%2), p=nextprime(1+p); mp = p*p, if(3==(n%4),mp *= p,m *= (mp-1)/(p-1))); n>>=1); (m); };
%o A324058 A324058(n) = gcd(A324054(n), A005940(1+n)*A106737(n));
%o A324058 \\ Alternatively as:
%o A324058 A324121(n) = gcd(sigma(n),n*numdiv(n));
%o A324058 A324058(n) = A324121(A005940(1+n));
%Y A324058 Cf. A000005, A000203, A005940, A038040, A106737, A324054, A324057, A324121.
%K A324058 nonn
%O A324058 0,3
%A A324058 _Antti Karttunen_, Feb 15 2019