A142591 Composite terms in A143578.

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

Offset: 1

Author

Leroy Quet, Aug 24 2008

Keywords

• nonn

Comments

Conjecture: This consists exactly of the semiprimes p*q for which p + q divides p*q + 1. - Mohamed Bouhamida, Aug 17 2009 (Comment edited by N. J. A. Sloane, Sep 01 2019.)

Links

• Robert Israel, Table of n, a(n) for n = 1..2100

Crossrefs

Cf. A143578.

Programs

Maple

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:
S; # Robert Israel, Sep 01 2019

Mathematica

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 *)

Extensions

More terms from M. F. Hasler, Aug 25 2008

a(33)-a(46) from Ray Chandler, Jun 21 2009