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A256151 Triangular numbers n such that sigma(n) is a square number. 4
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..40.

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

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Last modified January 23 00:58 EST 2018. Contains 298093 sequences.