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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Moree gives an effective version, see Theorem 1.

LINKS

Table of n, a(n) for n=1..55.

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 A193988 A124455

Adjacent sequences:  A295582 A295583 A295584 * A295586 A295587 A295588

KEYWORD

nonn,fini,full

AUTHOR

Charles R Greathouse IV, Nov 23 2017

STATUS

approved

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Last modified November 29 09:18 EST 2021. Contains 349416 sequences. (Running on oeis4.)