

A083674


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


7



1, 36, 45, 23220, 105111, 135460, 2492028, 5286126, 6604795, 14308575, 45025305, 50516326, 54742416, 99017628, 108125865, 152486916, 386767578, 1083567628, 1561818105, 3169234305, 5005551540, 5718242211, 6125307903, 6479715880
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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), 2340.


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 A291713
Adjacent sequences: A083671 A083672 A083673 * A083675 A083676 A083677


KEYWORD

nonn


AUTHOR

Shyam Sunder Gupta, Jun 15 2003


STATUS

approved



