A057421 Consider the solutions to k = a+b = x*y and a*b = k*(x+y) where k, a, b, x, and y are all positive integers, ordered by increasing k and, in case of ties, by increasing x. Sequence gives values of a*b.

1024, 1296, 1458, 2500, 2592, 3750, 3072, 6480, 11250, 15552, 14580, 52500, 22500, 46080, 57024, 163296, 78750, 101376, 306250, 291600, 473850, 453600, 1968750, 1305600, 2095632, 652500, 1632960, 13162500, 3442500, 2114100, 4353750, 28540512, 9722592, 20944170

Offset

1,1

Comments

In the table below, ties (i.e., multiple solutions with the same value of k) are identified with asterisks. (Two solutions correspond to k=500, and three to k=8100.)

Links

Table of n, a(n) for n=1..34.

Example

   n     k     a     b   x     y  a*b = a(n)
  --  ----  ----  ----  --  ----  ----------
   1    64    32    32   8     8        1024
   2    72    36    36   6    12        1296
   3    81    27    54   9     9        1458
   4   100    50    50   5    20        2500
   5   108    36    72   6    18        2592
   6   125    50    75   5    25        3750
   7   128    32    96   8    16        3072
   8   216    36   180  12    18        6480
   9   225    75   150   5    45       11250
  10   288    72   216   6    48       15552
  11   324    54   270   9    36       14580
  12  *500*  150   350   5   100       52500
  13  *500*   50   450  20    25       22500
  14   576    96   480   8    72       46080
  15   864    72   792  18    48       57024
  16   972   216   756   6   162      163296
  17  1125    75  1050  25    45       78750
  18  1152    96  1056  16    72      101376
  19  1225   350   875   5   245      306250
  20  1800   180  1620  12   150      291600
  21  2025   270  1755   9   225      473850
  22  2700   180  2520  18   150      453600
  23  3125   875  2250   5   625     1968750
  24  3200   480  2720   8   400     1305600
  25  3528   756  2772   6   588     2095632
  26  4500   150  4350  45   100      652500
  27  7776   216  7560  48   162     1632960
  28 *8100* 2250  5850   5  1620    13162500
  29 *8100*  450  7650  20   405     3442500
  30 *8100*  270  7830  36   225     2114100

Crossrefs

Cf. A057371.

Sequence in context: A235719 A365583 A057370 * A074211 A057443 A046313

Adjacent sequences: A057418 A057419 A057420 * A057422 A057423 A057424

Keyword

nonn

Author

Naohiro Nomoto, Sep 24 2000

Extensions

Edited by Jon E. Schoenfield, May 02 2021

More terms from Jinyuan Wang, May 02 2021

Status

approved