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A142591
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Composite terms in A143578.
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3
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15, 35, 95, 119, 143, 209, 287, 319, 323, 377, 527, 559, 779, 899, 923, 989, 1007, 1189, 1199, 1343, 1349, 1763, 1919, 2159, 2507, 2759, 2911, 3239, 3599, 3827, 4031, 4607, 5183, 5207, 5249, 5459, 5543, 6439, 6887, 7067, 7279, 7739, 8159, 8639, 9179, 9593
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OFFSET
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1,1
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COMMENTS
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Conjecture: This consists exactly of the semiprimes pq for which p + q divides pq + 1. - Mohamed Bouhamida, Aug 17 2009] (Comment edited by N. J. A. Sloane, Sep 01 2019.)
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LINKS
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MAPLE
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filter:= proc(n) local k, D, j, t;
D:= select(t -> t^2 <= n, numtheory:-divisors(n));
j:= max(D);
t:= j+n/j;
andmap(k -> (k+n/k) mod t = 0, D);
end proc:
count:= 0: S:= NULL:
for n from 2 while count < 100 do
if isprime(n) then next
elif filter(n) then
count:= count+1;
S:= S, n;
fi
od:
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MATHEMATICA
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Select[Reap[Module[{n, k}, For[n = 1, n < 10000, n++, k = Max[Select[Divisors[n], # <= Sqrt[n]&]]; If[Length[Union[ Mod[Divisors[n] + n/Divisors[n], k+n/k]]] == 1, Sow[n]]]]][[2, 1]], CompositeQ] (* Jean-François Alcover, Feb 07 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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