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a(n) = gcd((s+1)/2, 1+sigma(s)), where s is the n-th odd square, (2n-1)^2.
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%I #15 Aug 24 2020 22:28:36

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

%T 1,1,1,1,1,1,1,1,1,1,1,1,5,1,1,13,1,1,1,1,1,1,1,1,1,1,1,5,1,1,1,1,1,1,

%U 1,1,1,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,1,1,1,1,1,1,1,1,1,1,1,1

%N a(n) = gcd((s+1)/2, 1+sigma(s)), where s is the n-th odd square, (2n-1)^2.

%C See comments in A336700, A337337, and A337339.

%H Antti Karttunen, <a href="/A336697/b336697.txt">Table of n, a(n) for n = 1..16396</a>

%H Antti Karttunen, <a href="/A336697/a336697.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F For all n >= 1, a(A048673(n)) = A337337(n).

%t Array[GCD[(# + 1)/2, 1 + DivisorSigma[1, #]] &[(2 # - 1)^2] &, 120] (* _Michael De Vlieger_, Aug 24 2020 *)

%o (PARI) A336697(n) = { my(s=((n+n-1)^2)); gcd((s+1)/2,1+sigma(s)); };

%Y Cf. A000203, A016754, A048673, A336700, A337337, A337339.

%K nonn

%O 1,17

%A _Antti Karttunen_, Aug 18 2020