

A256151


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


5



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
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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, 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



