A225440 Triangular numbers that are the product of three distinct triangular numbers greater than 1.

378, 630, 990, 3240, 4095, 4950, 5460, 9180, 15400, 19110, 25200, 31878, 37128, 37950, 39060, 52650, 61425, 79800, 97020, 103740, 105570, 122265, 145530, 157080, 161028, 176715, 192510, 221445, 265356, 288420, 304590, 306936, 346528, 437580, 500500, 545490, 583740

Offset: 1

Author

Alex Ratushnyak, May 08 2013

Keywords

• nonn

Comments

Triangular numbers of the form triangular(x) * triangular(y) * triangular(z), x > y > z > 1.

Examples

			378 = 3 * 6 * 21.
630 = 3 * 10 * 21.
990 = 3 * 6 * 55.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000217, A085780, A140089, A188630, A225390.

Programs

C

#include 
typedef unsigned long long U64;
U64 isTriangular(U64 a) {  // ! Must be a < (1<<63)
    U64 s = sqrt(a*2);
    if (a>=(1ULL<<63)) exit(1);
    return (s*(s+1)/2 == a);
}
int compare64(const void *p1, const void *p2) {
  if (*(U64*)p1 == *(U64*)p2) return 0;
  if (*(U64*)p1 < *(U64*)p2) return -1;
  return 1;
}
#define TOP (1<<21)
U64 d[TOP];
int main() {
  U64 c, x, tx, y, ty, z, tz, p = 0;
    for (x = tx = 3; tx <= TOP; tx+=x, ++x) {
    for (y = ty = 3; ty < tx;   ty+=y, ++y) {
    for (z = tz = 3; tz < ty;   tz+=z, ++z) {
    c = tx*ty*tz;
    if (c <= TOP*18 && isTriangular(c))  d[p++] = c;
  }}}
  qsort(d, p, 8, compare64);
  for (x=c=0; cx) printf("%llu, ", y), x=y;
  return 0;
}