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a(n) = gcd(1+n-A020639(n), 1+sigma(n)-A020639(n)-n), where A020639 gives the smallest prime factor of n (and 1 for 1), and sigma is the sum of divisors of n.
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%I #7 Jun 12 2019 19:14:00

%S 1,1,1,1,1,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,27,1,1,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,5,1,1,1,7,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,5,1,1,1,1,5,1,1,1,7,5,1,1,1,1,1,1,1,1,1

%N a(n) = gcd(1+n-A020639(n), 1+sigma(n)-A020639(n)-n), where A020639 gives the smallest prime factor of n (and 1 for 1), and sigma is the sum of divisors of n.

%H Antti Karttunen, <a href="/A326073/b326073.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = gcd(1+n-A020639(n), 1+A000203(n)-A020639(n)-n).

%o (PARI)

%o A020639(n) = if(1==n, n, factor(n)[1, 1]);

%o A326073(n) = gcd(1+n-A020639(n), 1+sigma(n)-A020639(n)-n);

%Y Cf. A000203, A020639, A326074.

%Y Cf. also A009194, A325385, A325813, A325975, A326046, A326047, A326048, A326056, A326057, A326060, A326062, A326129, A326130, A326140, A326144, A326147.

%K nonn

%O 1,6

%A _Antti Karttunen_, Jun 10 2019