A083674 Triangular numbers whose sum of divisors is also a triangular number.

1, 36, 45, 23220, 105111, 135460, 2492028, 5286126, 6604795, 14308575, 45025305, 50516326, 54742416, 99017628, 108125865, 152486916, 386767578, 1083567628, 1561818105, 3169234305, 5005551540, 5718242211, 6125307903, 6479715880

Offset: 1

Author

Shyam Sunder Gupta, Jun 15 2003

Keywords

• nonn

Comments

1, 5286126, 45025305, 54742416, ... are also hexagonal and their sum of divisors too. - Michel Marcus, Apr 20 2014

Examples

			a(2)=36 because sum of divisors of 36 =1+2+3+4+6+9+12+18+36=91, which is also a triangular number.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..200
• Shyam Sunder Gupta, Fascinating Triangular Numbers.
• Douglas E. Iannucci, Florian Luca, Triangular numbers whose sum of divisors is also triangular, Acta Arithmetica 129(2007), 23-40.

Crossrefs

Cf. A008848 (similar, with squares).

Programs

Mathematica

Select[Accumulate[Range[120000]],OddQ[Sqrt[8*DivisorSigma[1,#]+1]]&] (* Harvey P. Dale, Feb 25 2015 *)

PARI

isok(n) = ispolygonal(n, 3) && ispolygonal(sigma(n), 3); \\ Michel Marcus, Apr 20 2014