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%I #25 Sep 08 2022 08:46:11
%S 1,3,66,210,820,2346,4278,22578,27966,32131,35511,51681,53956,102378,
%T 169653,173755,177906,223446,241860,256686,306153,310866,349866,
%U 431056,434778,470935,491536,512578,567645,579426,688551,799480,845650,893116,963966,1031766,1110795,1200475,1613706,1719585
%N Triangular numbers n such that sigma(n) is a square number.
%C This sequence is the intersection of A000217 and A006532.
%C The corresponding triangular indices are in A116990. - _Michel Marcus_, Mar 17 2015
%H Amiram Eldar, <a href="/A256151/b256151.txt">Table of n, a(n) for n = 1..10000</a>
%e 3 is in the sequence because 3=2*3/2 is triangular, and sigma(3)=1+3=4=2^2 is square.
%t Select[Accumulate[Range[0, 2000]], IntegerQ@Sqrt@DivisorSigma[1, #] &] (* _Michael De Vlieger_, Mar 17 2015 *)
%o (PARI) {for(i=1,2*10^3,n=i*(i+1)/2;if(issquare(sigma(n)),print1(n,", ")))}
%o (Magma) [n*(n+1) div 2: n in [1..2000] | IsSquare(SumOfDivisors(n*(n+1) div 2))]; // _Vincenzo Librandi_, Mar 17 2015
%Y Cf. A000290, A000217, A006532, A074285, A116990, A256149, A256150, A256152.
%K nonn
%O 1,2
%A _Antonio Roldán_, Mar 16 2015
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