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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.

%I A057421 #15 May 07 2021 01:15:58
%S A057421 1024,1296,1458,2500,2592,3750,3072,6480,11250,15552,14580,52500,
%T A057421 22500,46080,57024,163296,78750,101376,306250,291600,473850,453600,
%U A057421 1968750,1305600,2095632,652500,1632960,13162500,3442500,2114100,4353750,28540512,9722592,20944170
%N 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.
%C A057421 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.)
%e A057421    n     k     a     b   x     y  a*b = a(n)
%e A057421   --  ----  ----  ----  --  ----  ----------
%e A057421    1    64    32    32   8     8        1024
%e A057421    2    72    36    36   6    12        1296
%e A057421    3    81    27    54   9     9        1458
%e A057421    4   100    50    50   5    20        2500
%e A057421    5   108    36    72   6    18        2592
%e A057421    6   125    50    75   5    25        3750
%e A057421    7   128    32    96   8    16        3072
%e A057421    8   216    36   180  12    18        6480
%e A057421    9   225    75   150   5    45       11250
%e A057421   10   288    72   216   6    48       15552
%e A057421   11   324    54   270   9    36       14580
%e A057421   12  *500*  150   350   5   100       52500
%e A057421   13  *500*   50   450  20    25       22500
%e A057421   14   576    96   480   8    72       46080
%e A057421   15   864    72   792  18    48       57024
%e A057421   16   972   216   756   6   162      163296
%e A057421   17  1125    75  1050  25    45       78750
%e A057421   18  1152    96  1056  16    72      101376
%e A057421   19  1225   350   875   5   245      306250
%e A057421   20  1800   180  1620  12   150      291600
%e A057421   21  2025   270  1755   9   225      473850
%e A057421   22  2700   180  2520  18   150      453600
%e A057421   23  3125   875  2250   5   625     1968750
%e A057421   24  3200   480  2720   8   400     1305600
%e A057421   25  3528   756  2772   6   588     2095632
%e A057421   26  4500   150  4350  45   100      652500
%e A057421   27  7776   216  7560  48   162     1632960
%e A057421   28 *8100* 2250  5850   5  1620    13162500
%e A057421   29 *8100*  450  7650  20   405     3442500
%e A057421   30 *8100*  270  7830  36   225     2114100
%Y A057421 Cf. A057371.
%K A057421 nonn
%O A057421 1,1
%A A057421 _Naohiro Nomoto_, Sep 24 2000
%E A057421 Edited by _Jon E. Schoenfield_, May 02 2021
%E A057421 More terms from _Jinyuan Wang_, May 02 2021