A116541 Triangular numbers for which the number of divisors is also a triangular number.

1, 28, 45, 153, 171, 325, 496, 2016, 3321, 4753, 4950, 7260, 7381, 8256, 11628, 13203, 14196, 20100, 29161, 41616, 56953, 64620, 65341, 73536, 76636, 77028, 89676, 90100, 97461, 101475, 126756, 130816, 150975, 166176, 166753, 179700, 180300

Offset

1,2

Links

Gheorghe Coserea, Table of n, a(n) for n = 1..20000

Example

496 is in the sequence because it is a triangular number (31*32/2) and has 10=4*5/2 divisors (1,2,4,8,16,31,62,124,248,496).

Maple

with(numtheory): a:=proc(n) local s: s:=tau(n*(n+1)/2): if type(sqrt(1+8*s)/2-1/2, integer)=true then n*(n+1)/2 else fi end: seq(a(n), n=1..750); # Emeric Deutsch, Apr 06 2006

Mathematica

Select[Range[600]*Range[2, 601]/2, IntegerQ@ Sqrt[8 DivisorSigma[0, #] + 1] &] (* Robert G. Wilson v, Apr 20 2006 *)

Prog

(PARI)
seq(N) = {
  my(a = vector(N), n = 1, cnt=0);
  while (cnt < N,
        my(tn = n*(n+1)/2, d = numdiv(tn), x = (sqrtint(1+8*d)-1)\2);
        if (x*(x+1)/2 == d, a[cnt++] = tn); n++);
  return(a);
};
seq(37)  \\ Gheorghe Coserea, Jun 12 2016

Crossrefs

Cf. A000005, A000217.

Sequence in context: A144581 A075875 A332764 * A292989 A116565 A305060

Adjacent sequences: A116538 A116539 A116540 * A116542 A116543 A116544

Keyword

nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 03 2006

Extensions

More terms from Emeric Deutsch, Apr 06 2006

Typos in Mma program corrected by Giovanni Resta, Jun 12 2016

Status

approved