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%I #12 Aug 17 2021 00:09:03
%S 1,2,3,4,5,6,8,9,10,12,14,15,16,18,20,21,22,24,26,28,30,36,40,42,48,
%T 50,54,60,66,70,72,78,84,90,96,102,108,114,120,126,132,138,150,156,
%U 168,180,210,240,270,300,330,390,420,630,840
%N Numbers k such that Dirichlet's theorem has a purely elementary proof mod k via the Erdős method.
%C Moree gives an effective version, see Theorem 1.
%H Paul Erdős, <a href="https://eudml.org/doc/168561">Über die Primzahlen gewisser arithmetischer Reihen</a>, Math. Z. 39 (1935), pp. 473-491. [<a href="http://www.renyi.hu/~p_erdos/1935-10.pdf">alternate link</a>]
%H Martin Klazar, <a href="http://kam.mff.cuni.cz/~klazar/ln_antcII.pdf">Analytic and Combinatorial Number Theory II</a> (lecture notes). See section 2.3, Erdős's partial proof of Dirichlet's theorem.
%H P. Moree, <a href="https://doi.org/10.1016/0898-1221(93)90071-3">Bertrand's postulate for primes in arithmetical progressions</a>, Computers & Mathematics with Applications 26:5 (1993), pp. 35-43.
%F Numbers k such that Sum_{p < k, p does not divide k} 1/p < 1.
%e 15 is in the sequence since 1/2 + 1/7 + 1/11 + 1/13 = 1623/2002 < 1.
%o (PARI) is(n)=if(n>840, 0, my(s); forprime(p=2,n-1, if(n%p,s+=1/p)); s<1)
%K nonn,fini,full
%O 1,2
%A _Charles R Greathouse IV_, Nov 23 2017
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