A147571 Numbers with exactly 4 distinct prime divisors {2,3,5,7}.

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

Offset: 1

Author

Artur Jasinski, Nov 07 2008

Keywords

• nonn

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

Links

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

Crossrefs

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

Programs

Magma

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

Mathematica

a = {}; Do[If[EulerPhi[x]/x == 8/35, AppendTo[a, x]], {x, 1, 100000}]; a
Select[Range[20000],PrimeNu[#]==4&&Max[FactorInteger[#][[;;,1]]]<11&] (* Harvey P. Dale, Nov 05 2024 *)

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

Formula

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

Sum_{n>=1} 1/a(n) = 1/48. - Amiram Eldar, Nov 12 2020