A232619 Numbers k such that sigma(k) and sigma(2*k) are triangular numbers.
1, 3199808, 36210072, 48138616, 106449517, 109040509, 109903789, 110003837, 204102760401, 3050610977780, 3655577208308, 3660654715316, 3660725004788, 5607890017600, 6123048180800, 7412048520512, 7471435008064, 53218856249194, 53221469311786, 71505497845764, 103285924642372, 176553289677888, 176596975245888, 176600346573888
Offset: 1
Examples
sigma(3199808) = 6784086 = triangular(3683), sigma(3199808*2) = 13621590 = triangular(5219), so 3199808 is in the sequence.
Programs
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PARI
is(n)=issquare(8*sigma(n)+1)&&issquare(8*sigma(2*n)+1) \\ Ralf Stephan, Nov 30 2013
Extensions
a(9) from Hiroaki Yamanouchi, Oct 02 2014
Terms a(10) onward from Max Alekseyev, Feb 21 2024