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A329169 Numbers k such that k=(a+b)*c=a*b+c for more than one triple (a,b,c) with 1<c<a<=b. 1
3000, 4422, 22425, 25344, 35178, 44135, 49329, 81075, 128640, 143792, 154698, 182970, 291330, 341320, 389064, 413424, 451248, 581280, 593670, 638370, 662784, 686546, 714840, 807534, 891324, 905240, 906980, 934800, 1005039, 1072720, 1164672, 1326528, 1350174, 1369764, 1438080, 1478048, 1487525 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The first term with more than two triples is 38601360, corresponding to (a,b,c) = (1794, 21516, 1656), (3180, 12138, 2520) and (6015, 6417, 3105).

LINKS

Robert Israel, Table of n, a(n) for n = 1..162

EXAMPLE

a(3)=22425 is a member because we can take (a,b,c)=(149,150,75) or (42,533,39):

22425 = (149+150)*75 = 149*150+75 = (42+533)*39 = 42*533+39.

MAPLE

N:= 10^7: # for terms <= N

Res:= NULL:

for a from 3 to N/3 do

   for b from 3 to a while a*b < N do

     c:= a*b/(a+b-1);

     if c::posint and c>1 then

       v:= (a+b)*c;

       if v<=N then Res:= Res, v fi

     fi

od od:

S:= sort([Res]):

J:= select(i -> S[i+1]=S[i], [$1..nops(S)-1]):

sort(convert(convert(S[J], set), list));

CROSSREFS

Subsequence of A191676.

Sequence in context: A106766 A119892 A158861 * A236982 A202097 A229782

Adjacent sequences:  A329166 A329167 A329168 * A329170 A329171 A329172

KEYWORD

nonn

AUTHOR

Robert Israel, Nov 06 2019

STATUS

approved

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Last modified February 26 09:39 EST 2020. Contains 332277 sequences. (Running on oeis4.)