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%I #21 Sep 12 2017 02:41:07
%S 1,3,6,28,36,66,91,231,496,8128,14196,15225,129795,491536,780625,
%T 2476425,33550336,488265625,728302695,7403072040,8589869056,
%U 101548795116,134027094930,137438691328,5773115351325,22075617042480,28642840690815,61992314210541
%N Triangular numbers whose sum of aliquot divisors is also a triangular number.
%C Indices of these triangular numbers: {1, 2, 3, 7, 8, 11, 13, 21, 31, 127, 168, 174, 509, 991, 1249, 2225, 8191, 31249, 38165, 121680, 131071, 450663, 517739, 524287, 3397974, 6644639}. - _Robert G. Wilson v_, Apr 03 2006
%H Donovan Johnson, <a href="/A083675/b083675.txt">Table of n, a(n) for n = 1..40</a>
%H Shyam Sunder Gupta, <a href="http://www.shyamsundergupta.com/triangle.htm">Fascinating Triangular Numbers</a>.
%e a(5) = 66 because the sum of aliquot divisors of 66 = 1+2+3+6+11+22+33 = 78, which is also a triangular number.
%e 91 is in the sequence because it is a triangular number and the sum of its proper divisors, namely 1+7+13 = 21, is also a triangular number. - Luc Stevens (lms022(AT)yahoo.com), Apr 03 2006
%p with(numtheory): a:=proc(n) local sn: sn:=sigma(n*(n+1)/2)-n*(n+1)/2: if type(sqrt(1+8*sn)/ 2-1/2,integer)=true then n*(n+1)/2 else fi end: seq(a(n),n=1..180000); # _Emeric Deutsch_, Apr 03 2006
%t triQ[n_] := IntegerQ@Sqrt[8n + 1]; Do[ t = n(n + 1)/2; If[ triQ[DivisorSigma[1, t] - t], Print[t]], {n, 7*10^7}] (* _Robert G. Wilson v_, Apr 03 2006 *)
%o (PARI) for(n=1,1e6,if(ispolygonal(sigma(t=n*(n+1)/2)-t,3),print1(t", "))) \\ _Charles R Greathouse IV_, May 20 2013
%Y Cf. A000396.
%K nonn
%O 1,2
%A _Shyam Sunder Gupta_, Jun 15 2003
%E Added 1, merged with resubmission by L. Stevens of Apr 2006 - _R. J. Mathar_, Aug 08 2008
%E a(27)-a(28) from _Donovan Johnson_, Aug 11 2011
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