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

1,2

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000040, A211384.

Sequence in context: A023839 A004723 A293754 * A258022 A333638 A089590

Adjacent sequences: A242407 A242408 A242409 * A242411 A242412 A242413

Keyword

nonn

Author

J. Lowell, May 13 2014

Status

approved