cp's OEIS Frontend

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

%I A225390 #9 May 06 2013 15:05:00
%S A225390 630,749700,2162160,34283340,76576500,105887628,330360660,865924920,
%T A225390 2456409186,17246794950,35051708835,999302826060,3153804823260,
%U A225390 161708540211900,1153195485992550,1330786621788263640
%N A225390 Triangular numbers representable as Tx*Ty, where Tx>1 and Ty>1 are triangular numbers, in two or more ways.
%C A225390 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.
%o A225390 (C)
%o A225390 #include <stdio.h>
%o A225390 typedef unsigned long long U64;
%o A225390 U64 isTriangular(U64 a) {
%o A225390     U64 sr = 1ULL<<31, s, b;
%o A225390     while (a < sr*(sr+1)/2)  sr>>=1;
%o A225390     for (b = sr>>1; b; b>>=1) {
%o A225390         s = sr+b;
%o A225390         if (a >= s*(s+1)/2)  sr = s;
%o A225390     }
%o A225390     return (sr*(sr+1)/2 == a);
%o A225390 }
%o A225390 int main() {
%o A225390   U64 c, i, j, k, t;
%o A225390   for (i = t = 0; i < (1ULL<<32); i++) {
%o A225390     for (c=0, t += i, k = j = 3; k*k < t; k+=j, ++j)
%o A225390       if (t%k==0 && isTriangular(t/k)) ++c;
%o A225390     if (c>1) printf("%llu, ", t);
%o A225390   }
%o A225390   return 0;
%o A225390 }
%Y A225390 Cf. A000217, A188630.
%K A225390 nonn,hard,more
%O A225390 1,1
%A A225390 _Alex Ratushnyak_, May 06 2013
%E A225390 a(15)-a(16) from _Donovan Johnson_, May 06 2013