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Numbers k such that sigma(k) and sigma(2*k) are triangular numbers.
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%I #21 Feb 22 2024 02:13:30

%S 1,3199808,36210072,48138616,106449517,109040509,109903789,110003837,

%T 204102760401,3050610977780,3655577208308,3660654715316,3660725004788,

%U 5607890017600,6123048180800,7412048520512,7471435008064,53218856249194,53221469311786,71505497845764,103285924642372,176553289677888,176596975245888,176600346573888

%N Numbers k such that sigma(k) and sigma(2*k) are triangular numbers.

%e sigma(3199808) = 6784086 = triangular(3683), sigma(3199808*2) = 13621590 = triangular(5219), so 3199808 is in the sequence.

%o (PARI) is(n)=issquare(8*sigma(n)+1)&&issquare(8*sigma(2*n)+1) \\ _Ralf Stephan_, Nov 30 2013

%Y A subsequence of A045746.

%Y Cf. A000203, A000217, A232445.

%K nonn,hard

%O 1,2

%A _Alex Ratushnyak_, Nov 27 2013

%E a(9) from _Hiroaki Yamanouchi_, Oct 02 2014

%E Terms a(10) onward from _Max Alekseyev_, Feb 21 2024