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

1,2

Links

Table of n, a(n) for n=1..24.

Example

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

Prog

(PARI) is(n)=issquare(8*sigma(n)+1)&&issquare(8*sigma(2*n)+1) \\ Ralf Stephan, Nov 30 2013

Crossrefs

A subsequence of A045746.

Cf. A000203, A000217, A232445.

Sequence in context: A122034 A153750 A234689 * A223287 A223484 A029820

Adjacent sequences: A232616 A232617 A232618 * A232620 A232621 A232622

Keyword

nonn,hard

Author

Alex Ratushnyak, Nov 27 2013

Extensions

a(9) from Hiroaki Yamanouchi, Oct 02 2014

Terms a(10) onward from Max Alekseyev, Feb 21 2024

Status

approved