login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A083674 Triangular numbers whose sum of divisors is also a triangular number. 7

%I

%S 1,36,45,23220,105111,135460,2492028,5286126,6604795,14308575,

%T 45025305,50516326,54742416,99017628,108125865,152486916,386767578,

%U 1083567628,1561818105,3169234305,5005551540,5718242211,6125307903,6479715880

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

%C 1, 5286126, 45025305, 54742416, ... are also hexagonal and their sum of divisors too. - _Michel Marcus_, Apr 20 2014

%H Donovan Johnson, <a href="/A083674/b083674.txt">Table of n, a(n) for n = 1..200</a>

%H Shyam Sunder Gupta, <a href="http://www.shyamsundergupta.com/triangle.htm">Fascinating Triangular Numbers</a>.

%H Douglas E. Iannucci, Florian Luca, <a href="http://dx.doi.org/10.4064/aa129-1-2">Triangular numbers whose sum of divisors is also triangular</a>, Acta Arithmetica 129(2007), 23-40.

%e a(2)=36 because sum of divisors of 36 =1+2+3+4+6+9+12+18+36=91, which is also a triangular number.

%t Select[Accumulate[Range[120000]],OddQ[Sqrt[8*DivisorSigma[1,#]+1]]&] (* _Harvey P. Dale_, Feb 25 2015 *)

%o (PARI) isok(n) = ispolygonal(n, 3) && ispolygonal(sigma(n), 3); \\ _Michel Marcus_, Apr 20 2014

%Y Cf. A008848 (similar with squares).

%K nonn

%O 1,2

%A _Shyam Sunder Gupta_, Jun 15 2003

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 24 07:53 EST 2020. Contains 338607 sequences. (Running on oeis4.)