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 A225390 Triangular numbers representable as Tx*Ty, where Tx>1 and Ty>1 are triangular numbers, in two or more ways. 5
 630, 749700, 2162160, 34283340, 76576500, 105887628, 330360660, 865924920, 2456409186, 17246794950, 35051708835, 999302826060, 3153804823260, 161708540211900, 1153195485992550, 1330786621788263640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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. LINKS PROG (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; } CROSSREFS Cf. A000217, A188630. Sequence in context: A234241 A185849 A058832 * A061163 A045168 A270802 Adjacent sequences: A225387 A225388 A225389 * A225391 A225392 A225393 KEYWORD nonn,hard,more AUTHOR Alex Ratushnyak, May 06 2013 EXTENSIONS a(15)-a(16) from Donovan Johnson, May 06 2013 STATUS approved

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Last modified February 3 07:57 EST 2023. Contains 360024 sequences. (Running on oeis4.)