A275608 Numbers that divide no nonzero terms of A003422.

3, 6, 8, 9, 12, 13, 15, 16, 18, 20, 21, 24, 25, 26, 27, 28, 29, 30, 32, 33, 35, 36, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 69, 70, 72, 75, 76, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100

Offset: 1

Author

Robert Israel, Nov 14 2016

Keywords

• nonn

Comments

Numbers k such that A013584(k) = 0.

If k is in the sequence, then so is every multiple of k.

Examples

			3 is in the sequence because A003422(1)=1 and A003422(2)=2 are not divisible by 3, and A003422(k) == 1 (mod 3) for k >= 3.
4 is not in the sequence because A003422(3) = 4 is divisible by 4.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003422, A013584.

Complement of A049045.

Programs

Maple

filter:= proc(n) local t,r,m;
  r:= 1; t:= 1;
  for m from 1 do
    r:= r*m mod n;
    if r = 0 then return true fi;
    t:= t + r mod n;
    if t = 0 then return false fi;
  od;
end proc:
select(filter, [$2..100]);

Mathematica

okQ[n_] := Module[{t, r, m}, r = 1; t = 1; For[m = 1, True, m++, r = Mod[r*m, n]; If[r == 0, Return[True]]; t = Mod[t + r, n]; If[t == 0, Return[False]]]];
Select[Range[2, 100], okQ] (* Jean-François Alcover, Apr 12 2019, after Robert Israel *)