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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 26 16:27 EST 2020. Contains 338641 sequences. (Running on oeis4.)