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A242410 a(1)=1 and for n>1, a(n) is the smallest number greater than a(n-1) such that a(n) is not divisible by a(d) for any divisor d of n (except 1 and n).

%I A242410 #27 Jul 07 2017 15:14:42
%S A242410 1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,29,31,
%T A242410 33,34,37,38,41,42,43,44,45,46,47,48,49,50,51,52,53,54,57,58,59,60,61,
%U A242410 62,63,64,67,68,71,73,77,79,81,82,83,84
%N A242410 a(1)=1 and for n>1, a(n) is the smallest number greater than a(n-1) such that a(n) is not divisible by a(d) for any divisor d of n (except 1 and n).
%C A242410 Contains the primes (A000040). - _Robert Israel_, Jul 05 2017
%H A242410 Michael De Vlieger, <a href="/A242410/b242410.txt">Table of n, a(n) for n = 1..10000</a>
%e A242410 a(4) cannot be 4 because 4 is divisible by a(2) = 2. a(24) cannot be 25 because 25 is divisible by a(4) = 5.
%p A242410 f:= proc(n) option remember; local Q,k;
%p A242410      Q:= map(procname, numtheory:-divisors(n) minus {1,n});
%p A242410      for k from procname(n-1) + 1 do
%p A242410        if andmap(t -> (k mod t > 0), Q) then return k fi
%p A242410      od
%p A242410 end proc:
%p A242410 f(1):= 1:
%p A242410 map(f, [$1..100]); # _Robert Israel_, Jul 05 2017
%t A242410 a = {1}; Do[k = a[[n - 1]] + 1; While[AnyTrue[Most@ Rest@ Divisors@ n, Divisible[k, a[[#]] ] &], k++]; AppendTo[a, k], {n, 2, 61}]; a (* _Michael De Vlieger_, Jul 05 2017 *)
%o A242410 (PARI) okd(k, vd) = {for (i=1, #vd, if ((k % vd[i]) == 0, return (0));); return (1);}
%o A242410 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 A242410 lista(nn) = {va = vector(nn); va[1] = 1; for (n=2, nn, va[n] = fnext(n, va);); va;} \\ _Michel Marcus_, May 17 2014
%Y A242410 Cf. A000040, A211384.
%K A242410 nonn
%O A242410 1,2
%A A242410 _J. Lowell_, May 13 2014