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
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