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%I #6 May 08 2013 11:45:57
%S 378,630,990,3240,4095,4950,5460,9180,15400,19110,25200,31878,37128,
%T 37950,39060,52650,61425,79800,97020,103740,105570,122265,145530,
%U 157080,161028,176715,192510,221445,265356,288420,304590,306936,346528,437580,500500,545490,583740
%N Triangular numbers that are the product of three distinct triangular numbers greater than 1.
%C Triangular numbers of the form triangular(x) * triangular(y) * triangular(z), x > y > z > 1.
%H Donovan Johnson, <a href="/A225440/b225440.txt">Table of n, a(n) for n = 1..1000</a>
%e 378 = 3 * 6 * 21.
%e 630 = 3 * 10 * 21.
%e 990 = 3 * 6 * 55.
%o (C)
%o #include <stdio.h>
%o typedef unsigned long long U64;
%o U64 isTriangular(U64 a) { // ! Must be a < (1<<63)
%o U64 s = sqrt(a*2);
%o if (a>=(1ULL<<63)) exit(1);
%o return (s*(s+1)/2 == a);
%o }
%o int compare64(const void *p1, const void *p2) {
%o if (*(U64*)p1 == *(U64*)p2) return 0;
%o if (*(U64*)p1 < *(U64*)p2) return -1;
%o return 1;
%o }
%o #define TOP (1<<21)
%o U64 d[TOP];
%o int main() {
%o U64 c, x, tx, y, ty, z, tz, p = 0;
%o for (x = tx = 3; tx <= TOP; tx+=x, ++x) {
%o for (y = ty = 3; ty < tx; ty+=y, ++y) {
%o for (z = tz = 3; tz < ty; tz+=z, ++z) {
%o c = tx*ty*tz;
%o if (c <= TOP*18 && isTriangular(c)) d[p++] = c;
%o }}}
%o qsort(d, p, 8, compare64);
%o for (x=c=0; c<p; ++c) if ((y=d[c])>x) printf("%llu, ", y), x=y;
%o return 0;
%o }
%Y Cf. A000217, A085780, A140089, A188630, A225390.
%K nonn
%O 1,1
%A _Alex Ratushnyak_, May 08 2013
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