

A083675


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


6



1, 3, 6, 28, 36, 66, 91, 231, 496, 8128, 14196, 15225, 129795, 491536, 780625, 2476425, 33550336, 488265625, 728302695, 7403072040, 8589869056, 101548795116, 134027094930, 137438691328, 5773115351325, 22075617042480, 28642840690815, 61992314210541
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OFFSET

1,2


COMMENTS

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


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..40
Shyam Sunder Gupta, Fascinating Triangular Numbers.


EXAMPLE

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.
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


MAPLE

with(numtheory): a:=proc(n) local sn: sn:=sigma(n*(n+1)/2)n*(n+1)/2: if type(sqrt(1+8*sn)/ 21/2, integer)=true then n*(n+1)/2 else fi end: seq(a(n), n=1..180000); # Emeric Deutsch, Apr 03 2006


MATHEMATICA

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 *)


PROG

(PARI) for(n=1, 1e6, if(ispolygonal(sigma(t=n*(n+1)/2)t, 3), print1(t", "))) \\ Charles R Greathouse IV, May 20 2013


CROSSREFS

Cf. A000396.
Sequence in context: A287883 A246753 A247016 * A085076 A076711 A075088
Adjacent sequences: A083672 A083673 A083674 * A083676 A083677 A083678


KEYWORD

nonn


AUTHOR

Shyam Sunder Gupta, Jun 15 2003


EXTENSIONS

Added 1, merged with resubmission by L. Stevens of Apr 2006  R. J. Mathar, Aug 08 2008
a(27)a(28) from Donovan Johnson, Aug 11 2011


STATUS

approved



