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

1,2

Comments

This sequence is the intersection of A000217 and A006532.

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

Links

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

Example

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

Mathematica

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

Prog

(PARI) {for(i=1, 2*10^3, n=i*(i+1)/2; if(issquare(sigma(n)), print1(n, ", ")))}
(Magma) [n*(n+1) div 2: n in [1..2000] | IsSquare(SumOfDivisors(n*(n+1) div 2))]; // Vincenzo Librandi, Mar 17 2015

Crossrefs

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

Sequence in context: A028567 A003359 A292064 * A238471 A259457 A157543

Adjacent sequences: A256148 A256149 A256150 * A256152 A256153 A256154

Keyword

nonn

Author

Antonio Roldán, Mar 16 2015

Status

approved