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 A088915 Nonnegative numbers of the form mn(m+n) with integers m,n. 2
 0, 2, 6, 12, 16, 20, 30, 42, 48, 54, 56, 70, 72, 84, 90, 96, 110, 120, 126, 128, 132, 156, 160, 162, 180, 182, 198, 210, 240, 250, 264, 272, 286, 306, 308, 324, 330, 336, 342, 380, 384, 390, 420, 432, 448, 462, 468, 506, 510, 520, 540, 546, 552, 560, 576, 600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS These are the values of 3 X 3 Vandermonde determinants with integer entries. Solutions (m,n) are integral points on the elliptic curve m*n*(m+n)=a(n). Entries with record number of solutions are: 2, 6, 30, 240, 6480, 18480, 147840, 3991680 Possibly not minimal: a(n)=988159766157083520000000 has 22 solutions a(n)=2880932262848640000 20 solutions Multiplication of a(n) by u^3 does not decrease the number of solutions. [From Georgi Guninski, Oct 25 2010] Contribution from R. J. Mathar, Oct 24 2010: (Start) Examples of entries with more than one representation are: - 30 = 5*1*6 = 3*2*5, - 240 = 15*1*16 = 10*2*12 = 6*4*10, 6480 = 80*1*81 = 45*3*48 = 30*6*36 = 18*12*30, - 18408 = 77*3*80 = 66*4*70 = 48*7*55 = 30*14*44 = 22*20*42, - 147840 = 384*1*385 = 154*6*160 = 132*8*140 = 96*14*110 = 60*28*88 = 44*40*84 (6 representations), - 110270160 = 6*4284*4290 = 60*1326*1386 = 66*1260*1326 = 102*990*1092 = ... with 8 representations. (End) LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 MAPLE filter:= proc(n) local d, nd, x, y;   d:= numtheory:-divisors(n);   nd:= nops(d);   for x from 1 to nd do     for y from 1 to x do       if d[x]*d[y]*(d[x]+d[y])=n then return true fi   od od:   false end proc: filter(0):= 0: select(filter, [seq(i, i=0..1000, 2)]); # Robert Israel, Jul 24 2018 MATHEMATICA Select[Range[0, 600], {} != FindInstance[m n (m + n) == # && n >= 0 && m >= 0, {m, n}, Integers, 1] &] (* Giovanni Resta, Jul 24 2018 *) CROSSREFS Cf. A121741. Sequence in context: A263546 A143408 A191331 * A084790 A130237 A053457 Adjacent sequences:  A088912 A088913 A088914 * A088916 A088917 A088918 KEYWORD nonn AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 29 2003 EXTENSIONS More terms from Hugo Pfoertner, Apr 10 2004 STATUS approved

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Last modified June 13 09:02 EDT 2021. Contains 344981 sequences. (Running on oeis4.)