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A083674 Triangular numbers whose sum of divisors is also a triangular number. 7


%S 1,36,45,23220,105111,135460,2492028,5286126,6604795,14308575,

%T 45025305,50516326,54742416,99017628,108125865,152486916,386767578,

%U 1083567628,1561818105,3169234305,5005551540,5718242211,6125307903,6479715880

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

%C 1, 5286126, 45025305, 54742416, ... are also hexagonal and their sum of divisors too. - _Michel Marcus_, Apr 20 2014

%H Donovan Johnson, <a href="/A083674/b083674.txt">Table of n, a(n) for n = 1..200</a>

%H Shyam Sunder Gupta, <a href="http://www.shyamsundergupta.com/triangle.htm">Fascinating Triangular Numbers</a>.

%H Douglas E. Iannucci, Florian Luca, <a href="http://dx.doi.org/10.4064/aa129-1-2">Triangular numbers whose sum of divisors is also triangular</a>, Acta Arithmetica 129(2007), 23-40.

%e 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.

%t Select[Accumulate[Range[120000]],OddQ[Sqrt[8*DivisorSigma[1,#]+1]]&] (* _Harvey P. Dale_, Feb 25 2015 *)

%o (PARI) isok(n) = ispolygonal(n, 3) && ispolygonal(sigma(n), 3); \\ _Michel Marcus_, Apr 20 2014

%Y Cf. A008848 (similar with squares).

%K nonn

%O 1,2

%A _Shyam Sunder Gupta_, Jun 15 2003

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Last modified November 24 07:53 EST 2020. Contains 338607 sequences. (Running on oeis4.)