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A049045 Domain of A049044.

%I A049045 #13 Apr 10 2019 08:36:00
%S A049045 1,2,4,5,7,10,11,14,17,19,22,23,31,34,37,38,41,46,61,62,71,73,74,77,
%T A049045 82,89,103,113,122,131,139,142,146,154,157,163,167,173,178,191,193,
%U A049045 197,206,211,226,227,233,239,251,257,262,263,278,283,293,307,313,314,317
%N A049045 Domain of A049044.
%C A049045 Positive integers that divide some positive element of A003422.
%C A049045 From _Robert Israel_, Nov 14 2016: (Start)
%C A049045 Numbers n such that A013584(n) > 0.
%C A049045 If n is in the sequence, then so are all divisors of n. (End)
%H A049045 Robert Israel, <a href="/A049045/b049045.txt">Table of n, a(n) for n = 1..10000</a>
%p A049045 filter:= proc(n) local t,r,m;
%p A049045   r:= 1; t:= 1;
%p A049045   for m from 1 do
%p A049045     r:= r*m mod n;
%p A049045     if r = 0 then return false fi;
%p A049045     t:= t + r mod n;
%p A049045     if t = 0 then return true fi;
%p A049045   od;
%p A049045 end proc:
%p A049045 filter(1):= true:
%p A049045 select(filter, [$1..1000]); # _Robert Israel_, Nov 14 2016
%t A049045 okQ[n_] := Module[{t, r, m}, r = 1; t = 1; For[m = 1, True, m++, r = Mod[r*m, n]; If[r == 0, Return[False]]; t = Mod[t + r, n]; If[t == 0, Return[True]]]];
%t A049045 okQ[1] = True;
%t A049045 Select[Range[1000], okQ] (* _Jean-François Alcover_, Apr 10 2019, after _Robert Israel_ *)
%Y A049045 A049044, A003422, A013584.
%Y A049045 Complement of A275608.
%K A049045 nonn
%O A049045 1,2
%A A049045 _David W. Wilson_