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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.
1
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.)
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
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