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A225390
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Triangular numbers representable as Tx*Ty, where Tx>1 and Ty>1 are triangular numbers, in two or more ways.
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5
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630, 749700, 2162160, 34283340, 76576500, 105887628, 330360660, 865924920, 2456409186, 17246794950, 35051708835, 999302826060, 3153804823260, 161708540211900, 1153195485992550, 1330786621788263640
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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PROG
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(C)
#include <stdio.h>
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;
}
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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