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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

Table of n, a(n) for n=1..16.

PROG

(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;

}

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 29 03:18 EST 2020. Contains 332353 sequences. (Running on oeis4.)