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A275608 Numbers that divide no nonzero terms of A003422.

%I A275608 #17 Feb 18 2021 00:35:23
%S A275608 3,6,8,9,12,13,15,16,18,20,21,24,25,26,27,28,29,30,32,33,35,36,39,40,
%T A275608 42,43,44,45,47,48,49,50,51,52,53,54,55,56,57,58,59,60,63,64,65,66,67,
%U A275608 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
%N A275608 Numbers that divide no nonzero terms of A003422.
%C A275608 Numbers k such that A013584(k) = 0.
%C A275608 If k is in the sequence, then so is every multiple of k.
%H A275608 Robert Israel, <a href="/A275608/b275608.txt">Table of n, a(n) for n = 1..10000</a>
%e A275608 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.
%e A275608 4 is not in the sequence because A003422(3) = 4 is divisible by 4.
%p A275608 filter:= proc(n) local t,r,m;
%p A275608   r:= 1; t:= 1;
%p A275608   for m from 1 do
%p A275608     r:= r*m mod n;
%p A275608     if r = 0 then return true fi;
%p A275608     t:= t + r mod n;
%p A275608     if t = 0 then return false fi;
%p A275608   od;
%p A275608 end proc:
%p A275608 select(filter, [$2..100]);
%t A275608 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]]]];
%t A275608 Select[Range[2, 100], okQ] (* _Jean-François Alcover_, Apr 12 2019, after _Robert Israel_ *)
%Y A275608 Cf. A003422, A013584.
%Y A275608 Complement of A049045.
%K A275608 nonn
%O A275608 1,1
%A A275608 _Robert Israel_, Nov 14 2016