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).

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, 33, 34, 37, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 58, 59, 60, 61, 62, 63, 64, 67, 68, 71, 73, 77, 79, 81, 82, 83, 84

Offset: 1

Author

J. Lowell, May 13 2014

Keywords

• nonn

Comments

Contains the primes (A000040). - Robert Israel, Jul 05 2017

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A211384.

Programs

Maple

f:= proc(n) option remember; local Q,k;
     Q:= map(procname, numtheory:-divisors(n) minus {1,n});
     for k from procname(n-1) + 1 do
       if andmap(t -> (k mod t > 0), Q) then return k fi
     od
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Jul 05 2017

Mathematica

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 *)

PARI

okd(k, vd) = {for (i=1, #vd, if ((k % vd[i]) == 0, return (0));); return (1);}
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;}
lista(nn) = {va = vector(nn); va[1] = 1; for (n=2, nn, va[n] = fnext(n, va);); va;} \\ Michel Marcus, May 17 2014