%I #22 Jul 07 2017 15:14:11
%S 4,25,26,27,28,30,32,35,36,39,40,55,56,65,66,69,70,72,74,75,76,78,80,
%T 95,96,105,106,108,110,114,116,121,122,123,124,126,128,132,134,135,
%U 136,140,141,143,144,145,146,147,148,153,154,155,156,161,162,165,166
%N Complement of A242410.
%C 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 Robert Israel, <a href="/A289273/b289273.txt">Table of n, a(n) for n = 1..10000</a>
%p A242410:= proc(n) option remember; local Q,k;
%p Q:= map(procname, numtheory:-divisors(n) minus {1,n});
%p for k from procname(n-1) + 1 do
%p if andmap(t -> (k mod t > 0), Q) then return k fi
%p od
%p end proc:
%p A242410(1):= 1:
%p sort(convert({$1..A242410(1000)} minus map(A242410, {$1..1000}), list)); # _Robert Israel_, Jul 05 2017
%t 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 (PARI) okd(k, vd) = {for (i=1, #vd, if ((k % vd[i]) == 0, return (0)); ); return (1); }
%o 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 lista(nn) = {va = vector(nn); va[1] = 1; for (n=2, nn, va[n] = fnext(n, va); ); va; }
%Y Cf. A242410.
%K nonn
%O 1,1
%A _J. Lowell_, Jun 30 2017