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

Author

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

Keywords

• nonn

Examples

			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).
		

Links

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

Crossrefs

Cf. A000005, A000217.

Programs

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 *)

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

Extensions

More terms from Emeric Deutsch, Apr 06 2006

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