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A083674 Triangular numbers whose sum of divisors is also a triangular number. 5
1, 36, 45, 23220, 105111, 135460, 2492028, 5286126, 6604795, 14308575, 45025305, 50516326, 54742416, 99017628, 108125865, 152486916, 386767578, 1083567628, 1561818105, 3169234305, 5005551540, 5718242211, 6125307903, 6479715880 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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.

EXAMPLE

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.

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A008848 (similar with squares).

Sequence in context: A264961 A188630 A167310 * A160063 A260927 A244326

Adjacent sequences:  A083671 A083672 A083673 * A083675 A083676 A083677

KEYWORD

nonn

AUTHOR

Shyam Sunder Gupta, Jun 15 2003

STATUS

approved

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Last modified July 25 04:48 EDT 2017. Contains 289779 sequences.