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