A225390 Triangular numbers representable as Tx*Ty, where Tx>1 and Ty>1 are triangular numbers, in two or more ways.

630, 749700, 2162160, 34283340, 76576500, 105887628, 330360660, 865924920, 2456409186, 17246794950, 35051708835, 999302826060, 3153804823260, 161708540211900, 1153195485992550, 1330786621788263640

Offset: 1

Author

Alex Ratushnyak, May 06 2013

Keywords

• nonn
• hard
• more

Comments

Triangular numbers t such that there are four triangular numbers t1, t2, t3, t4, all bigger than 1, such that t = t1 * t2 = t3 * t4.

Crossrefs

Cf. A000217, A188630.

Programs

C

#include 
typedef unsigned long long U64;
U64 isTriangular(U64 a) {
    U64 sr = 1ULL<<31, s, b;
    while (a < sr*(sr+1)/2)  sr>>=1;
    for (b = sr>>1; b; b>>=1) {
        s = sr+b;
        if (a >= s*(s+1)/2)  sr = s;
    }
    return (sr*(sr+1)/2 == a);
}
int main() {
  U64 c, i, j, k, t;
  for (i = t = 0; i < (1ULL<<32); i++) {
    for (c=0, t += i, k = j = 3; k*k < t; k+=j, ++j)
      if (t%k==0 && isTriangular(t/k)) ++c;
    if (c>1) printf("%llu, ", t);
  }
  return 0;
}

Extensions

a(15)-a(16) from Donovan Johnson, May 06 2013