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A295585
Numbers k such that Dirichlet's theorem has a purely elementary proof mod k via the Erdős method.
0
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, 50, 54, 60, 66, 70, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 150, 156, 168, 180, 210, 240, 270, 300, 330, 390, 420, 630, 840
OFFSET
1,2
COMMENTS
Moree gives an effective version, see Theorem 1.
LINKS
Paul Erdős, Über die Primzahlen gewisser arithmetischer Reihen, Math. Z. 39 (1935), pp. 473-491. [alternate link]
Martin Klazar, Analytic and Combinatorial Number Theory II (lecture notes). See section 2.3, Erdős's partial proof of Dirichlet's theorem.
P. Moree, Bertrand's postulate for primes in arithmetical progressions, Computers & Mathematics with Applications 26:5 (1993), pp. 35-43.
FORMULA
Numbers k such that Sum_{p < k, p does not divide k} 1/p < 1.
EXAMPLE
15 is in the sequence since 1/2 + 1/7 + 1/11 + 1/13 = 1623/2002 < 1.
PROG
(PARI) is(n)=if(n>840, 0, my(s); forprime(p=2, n-1, if(n%p, s+=1/p)); s<1)
CROSSREFS
Sequence in context: A225734 A225733 A225732 * A324578 A373847 A193988
KEYWORD
nonn,fini,full
AUTHOR
STATUS
approved