A083675 Triangular numbers whose sum of aliquot divisors is also a triangular number.

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

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)/ 2-1/2, 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