A115909 Numbers k such that sigma(k)*k is a triangular number.

1, 2, 4, 8, 16, 32, 57, 64, 65, 85, 87, 128, 256, 512, 1024, 1245, 1421, 2048, 3146, 3330, 3790, 4096, 6695, 7257, 8192, 10137, 16384, 25884, 32768, 34420, 34551, 34947, 65536, 131072, 208495, 262144, 348161, 440495, 524288, 530270, 534430

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn

Comments

Infinite, since all the powers of 2 belong to the sequence.

Examples

			sigma(1421)*1421 = 2429910 = T(2204).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A064987, A000217, A115904, A115910.

Programs

Mathematica

Select[Range[540000],IntegerQ[(Sqrt[1+8(#*DivisorSigma[1,#])]-1)/2]&] (* Harvey P. Dale, Dec 16 2011 *)

PARI

isok(n) = ispolygonal(n*sigma(n), 3); \\ Amiram Eldar, Apr 06 2023