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%I #14 Nov 07 2019 12:20:25
%S 3000,4422,22425,25344,35178,44135,49329,81075,128640,143792,154698,
%T 182970,291330,341320,389064,413424,451248,581280,593670,638370,
%U 662784,686546,714840,807534,891324,905240,906980,934800,1005039,1072720,1164672,1326528,1350174,1369764,1438080,1478048,1487525
%N Numbers k such that k=(a+b)*c=a*b+c for more than one triple (a,b,c) with 1<c<a<=b.
%C 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).
%H Robert Israel, <a href="/A329169/b329169.txt">Table of n, a(n) for n = 1..162</a>
%e a(3)=22425 is a member because we can take (a,b,c)=(149,150,75) or (42,533,39):
%e 22425 = (149+150)*75 = 149*150+75 = (42+533)*39 = 42*533+39.
%p N:= 10^7: # for terms <= N
%p Res:= NULL:
%p for a from 3 to N/3 do
%p for b from 3 to a while a*b < N do
%p c:= a*b/(a+b-1);
%p if c::posint and c>1 then
%p v:= (a+b)*c;
%p if v<=N then Res:= Res, v fi
%p fi
%p od od:
%p S:= sort([Res]):
%p J:= select(i -> S[i+1]=S[i], [$1..nops(S)-1]):
%p sort(convert(convert(S[J],set),list));
%Y Subsequence of A191676.
%K nonn
%O 1,1
%A _Robert Israel_, Nov 06 2019
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