cp's OEIS Frontend

A337337 a(n) = gcd(1+sigma(s), (s+1)/2), where s is the square of n once prime-shifted (s = A003961(n)^2 = A003961(n^2)).

%I A337337 #18 Aug 25 2020 09:44:57
%S A337337 1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,1,1,1,1,1,1,1,1,1,1,1,1,13,1,1,1,1,1,1,
%T A337337 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,5,1,1,1,1,1,1,1,1,1,1,
%U A337337 1,1,1,1,1,5,1,1,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,17,1,1,1
%N A337337 a(n) = gcd(1+sigma(s), (s+1)/2), where s is the square of n once prime-shifted (s = A003961(n)^2 = A003961(n^2)).
%C A337337 All terms are in A007310, because all terms of A337336 are.
%H A337337 Antti Karttunen, <a href="/A337337/b337337.txt">Table of n, a(n) for n = 1..65537</a>
%H A337337 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A337337 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A337337 a(n) = gcd((s+1)/2, 1+sigma(s)), where s = A003961(n)^2 = A003961(n^2).
%F A337337 a(n) = gcd(A048673(n^2), 1+A003973(n^2)).
%F A337337 a(n) = gcd(A048673(n^2), A337194(A003961(n)^2)) = gcd(A337336(n), A336844(n^2)).
%F A337337 a(n) = A336697(A048673(n)).
%F A337337 a(n) = A337335(n^2).
%o A337337 (PARI)
%o A337337 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A337337 A337337(n) = { my(s=(A003961(n)^2)); gcd((s+1)/2, 1+sigma(s)); };
%o A337337 (PARI)
%o A337337 A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; };
%o A337337 A336697(n) = { my(s=((n+n-1)^2)); gcd((s+1)/2, 1+sigma(s)); };
%o A337337 A337337(n) = A336697(A048673(n));
%Y A337337 Cf. A003961, A003973, A007310, A048673, A336697, A336844, A337194, A337335, A337336, A337338, A337339.
%K A337337 nonn
%O A337337 1,14
%A A337337 _Antti Karttunen_, Aug 24 2020