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A289273 Complement of A242410.

%I A289273 #22 Jul 07 2017 15:14:11
%S A289273 4,25,26,27,28,30,32,35,36,39,40,55,56,65,66,69,70,72,74,75,76,78,80,
%T A289273 95,96,105,106,108,110,114,116,121,122,123,124,126,128,132,134,135,
%U A289273 136,140,141,143,144,145,146,147,148,153,154,155,156,161,162,165,166
%N A289273 Complement of A242410.
%C A289273 Conjecture: there will never be a point where this sequence has more terms than A242410. (80 is only the 21st term of this sequence.)
%H A289273 Robert Israel, <a href="/A289273/b289273.txt">Table of n, a(n) for n = 1..10000</a>
%p A289273 A242410:= proc(n) option remember; local Q,k;
%p A289273      Q:= map(procname, numtheory:-divisors(n) minus {1,n});
%p A289273      for k from procname(n-1) + 1 do
%p A289273        if andmap(t -> (k mod t > 0), Q) then return k fi
%p A289273      od
%p A289273 end proc:
%p A289273 A242410(1):= 1:
%p A289273 sort(convert({$1..A242410(1000)} minus map(A242410, {$1..1000}), list)); # _Robert Israel_, Jul 05 2017
%t A289273 a = {1}; Do[k = a[[n - 1]] + 1; While[AnyTrue[Most@ Rest@ Divisors@ n, Divisible[k, a[[#]] ] &], k++]; AppendTo[a, k], {n, 2, 110}]; Complement[Range@ Max@ a, a] (* _Michael De Vlieger_, Jul 05 2017 *)
%o A289273 (PARI) okd(k, vd) = {for (i=1, #vd, if ((k % vd[i]) == 0, return (0)); ); return (1); }
%o A289273 fnext(n, va) = {d = divisors(n); vd = vector(#d-2, i, va[d[i+1]]); k = va[n-1]+1; while (! okd(k, vd), k++); k; }
%o A289273 lista(nn) = {va = vector(nn); va[1] = 1; for (n=2, nn, va[n] = fnext(n, va); ); va; }
%Y A289273 Cf. A242410.
%K A289273 nonn
%O A289273 1,1
%A A289273 _J. Lowell_, Jun 30 2017