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

1,1

Comments

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

Links

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

Example

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

Prog

(C)
#include <stdio.h>
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; c<p; ++c) if ((y=d[c])>x) printf("%llu, ", y), x=y;
  return 0;
}

Crossrefs

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

Sequence in context: A030029 A064242 A116339 * A098840 A065702 A132648

Adjacent sequences: A225437 A225438 A225439 * A225441 A225442 A225443

Keyword

nonn

Author

Alex Ratushnyak, May 08 2013

Status

approved