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