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Search: id:A083675
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| A083675 |
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Triangular numbers whose sum of aliquot divisors is also a triangular number. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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 (rgwv(at)rgwv.com), Apr 03 2006
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LINKS
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Shyam Sunder Gupta, Fascinating Triangular Numbers.
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EXAMPLE
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a(5)=66 because 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
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MAPLE
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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 (deutsch(AT)duke.poly.edu), Apr 03 2006
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A000396.
Sequence in context: A060170 A097678 A074894 this_sequence A085076 A076711 A075088
Adjacent sequences: A083672 A083673 A083674 this_sequence A083676 A083677 A083678
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KEYWORD
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nonn
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AUTHOR
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Shyam Sunder Gupta (guptass(AT)rediffmail.com), Jun 15 2003
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EXTENSIONS
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Added 1, merged with resubmission by L. Stevens of Apr 2006 - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 08 2008
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