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A147571 Numbers with exactly 4 distinct prime divisors {2,3,5,7}. 13
210, 420, 630, 840, 1050, 1260, 1470, 1680, 1890, 2100, 2520, 2940, 3150, 3360, 3780, 4200, 4410, 5040, 5250, 5670, 5880, 6300, 6720, 7350, 7560, 8400, 8820, 9450, 10080, 10290, 10500, 11340, 11760, 12600, 13230, 13440, 14700, 15120, 15750, 16800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Successive numbers k such that EulerPhi[x]/x = m

( Family of sequences for successive n primes )

m=1/2 numbers with exactly 1 distinct prime divisor {2} see A000079

m=1/3 numbers with exactly 2 distinct prime divisors {2,3} see A033845

m=4/15 numbers with exactly 3 distinct prime divisors {2,3,5} see A143207

m=8/35 numbers with exactly 4 distinct prime divisors {2,3,5,7} see A147571

m=16/77 numbers with exactly 5 distinct prime divisors {2,3,5,7,11} see A147572

m=192/1001 numbers with exactly 6 distinct prime divisors {2,3,5,7,11,13} see A147573

m=3072/17017 numbers with exactly 7 distinct prime divisors {2,3,5,7,11,13,17} see A147574

m=55296/323323 numbers with exactly 8 distinct prime divisors {2,3,5,7,11,13,17,19} see A147575

k-th cyclotomic polynomial with exactly 17 negative coefficients (see A086780). - Paolo P. Lava, May 10 2019

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10688

FORMULA

a(n) = 210 * A002473(n). - David A. Corneth, May 14 2019

MAPLE

with(numtheory): P:=proc(n) local x; if nops(select(x->x<0, [coeffs(cyclotomic(n, x))]))=17 then n; fi; end: seq(P(j), j=1..16800); # Paolo P. Lava, May 10 2019

MATHEMATICA

a = {}; Do[If[EulerPhi[x]/x == 8/35, AppendTo[a, x]], {x, 1, 100000}]; a

PROG

(MAGMA) [n: n in [1..2*10^4] | PrimeDivisors(n) eq [2, 3, 5, 7]]; // Vincenzo Librandi, Sep 15 2015

(PARI) is(n)=n%210==0 && n==2^valuation(n, 2) * 3^valuation(n, 3) * 5^valuation(n, 5) * 7^valuation(n, 7) \\ Charles R Greathouse IV, Jun 19 2016

CROSSREFS

Cf. A002473, A086780, A143207, A147572, A147573, A147574, A147575, A147576, A147577, A147578, A147579, A147580.

Sequence in context: A258359 A325991 A264664 * A306508 A254466 A235304

Adjacent sequences:  A147568 A147569 A147570 * A147572 A147573 A147574

KEYWORD

nonn

AUTHOR

Artur Jasinski, Nov 07 2008

STATUS

approved

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Last modified October 20 07:33 EDT 2019. Contains 328252 sequences. (Running on oeis4.)