A256151 Triangular numbers n such that sigma(n) is a square number.

1, 3, 66, 210, 820, 2346, 4278, 22578, 27966, 32131, 35511, 51681, 53956, 102378, 169653, 173755, 177906, 223446, 241860, 256686, 306153, 310866, 349866, 431056, 434778, 470935, 491536, 512578, 567645, 579426, 688551, 799480, 845650, 893116, 963966, 1031766, 1110795, 1200475, 1613706, 1719585

Offset: 1

Author

Antonio Roldán, Mar 16 2015

Keywords

• nonn

Comments

This sequence is the intersection of A000217 and A006532.

The corresponding triangular indices are in A116990. - Michel Marcus, Mar 17 2015

Examples

			3 is in the sequence because 3=2*3/2 is triangular, and sigma(3)=1+3=4=2^2 is square.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A000217, A006532, A074285, A116990, A256149, A256150, A256152.

Programs

Magma

[n*(n+1) div 2: n in [1..2000] | IsSquare(SumOfDivisors(n*(n+1) div 2))]; // Vincenzo Librandi, Mar 17 2015

Mathematica

Select[Accumulate[Range[0, 2000]], IntegerQ@Sqrt@DivisorSigma[1, #] &] (* Michael De Vlieger, Mar 17 2015 *)

PARI

{for(i=1,2*10^3,n=i*(i+1)/2;if(issquare(sigma(n)),print1(n,", ")))}