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A225440 Triangular numbers that are the product of three distinct triangular numbers greater than 1. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 19 11:11 EDT 2019. Contains 322260 sequences. (Running on oeis4.)