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A142591 Composite terms in A143578.

%I A142591 #22 Oct 01 2024 20:41:00
%S A142591 15,35,95,119,143,209,287,319,323,377,527,559,779,899,923,989,1007,
%T A142591 1189,1199,1343,1349,1763,1919,2159,2507,2759,2911,3239,3599,3827,
%U A142591 4031,4607,5183,5207,5249,5459,5543,6439,6887,7067,7279,7739,8159,8639,9179,9593
%N A142591 Composite terms in A143578.
%C A142591 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.)
%H A142591 Robert Israel, <a href="/A142591/b142591.txt">Table of n, a(n) for n = 1..2100</a>
%p A142591 filter:= proc(n) local k,D,j,t;
%p A142591   D:= select(t -> t^2 <= n, numtheory:-divisors(n));
%p A142591   j:= max(D);
%p A142591   t:= j+n/j;
%p A142591   andmap(k -> (k+n/k) mod t = 0, D);
%p A142591 end proc:
%p A142591 count:= 0: S:= NULL:
%p A142591 for n from 2  while count < 100 do
%p A142591   if  isprime(n) then next
%p A142591   elif filter(n) then
%p A142591     count:= count+1;
%p A142591     S:= S, n;
%p A142591   fi
%p A142591 od:
%p A142591 S; # _Robert Israel_, Sep 01 2019
%t A142591 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 *)
%Y A142591 Cf. A143578.
%K A142591 nonn
%O A142591 1,1
%A A142591 _Leroy Quet_, Aug 24 2008
%E A142591 More terms from _M. F. Hasler_, Aug 25 2008
%E A142591 a(33)-a(46) from _Ray Chandler_, Jun 21 2009