cp's OEIS Frontend

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

%I A147571 #38 Nov 05 2024 14:48:12
%S A147571 210,420,630,840,1050,1260,1470,1680,1890,2100,2520,2940,3150,3360,
%T A147571 3780,4200,4410,5040,5250,5670,5880,6300,6720,7350,7560,8400,8820,
%U A147571 9450,10080,10290,10500,11340,11760,12600,13230,13440,14700,15120,15750,16800
%N A147571 Numbers with exactly 4 distinct prime divisors {2,3,5,7}.
%C A147571 Successive numbers k such that EulerPhi(x)/x = m:
%C A147571 ( Family of sequences for successive n primes )
%C A147571 m=1/2 numbers with exactly 1 distinct prime divisor {2} see A000079
%C A147571 m=1/3 numbers with exactly 2 distinct prime divisors {2,3} see A033845
%C A147571 m=4/15 numbers with exactly 3 distinct prime divisors {2,3,5} see A143207
%C A147571 m=8/35 numbers with exactly 4 distinct prime divisors {2,3,5,7} see A147571
%C A147571 m=16/77 numbers with exactly 5 distinct prime divisors {2,3,5,7,11} see A147572
%C A147571 m=192/1001 numbers with exactly 6 distinct prime divisors {2,3,5,7,11,13} see A147573
%C A147571 m=3072/17017 numbers with exactly 7 distinct prime divisors {2,3,5,7,11,13,17} see A147574
%C A147571 m=55296/323323 numbers with exactly 8 distinct prime divisors {2,3,5,7,11,13,17,19} see A147575
%H A147571 David A. Corneth, <a href="/A147571/b147571.txt">Table of n, a(n) for n = 1..10688</a>
%F A147571 a(n) = 210 * A002473(n). - _David A. Corneth_, May 14 2019
%F A147571 Sum_{n>=1} 1/a(n) = 1/48. - _Amiram Eldar_, Nov 12 2020
%t A147571 a = {}; Do[If[EulerPhi[x]/x == 8/35, AppendTo[a, x]], {x, 1, 100000}]; a
%t A147571 Select[Range[20000],PrimeNu[#]==4&&Max[FactorInteger[#][[;;,1]]]<11&] (* _Harvey P. Dale_, Nov 05 2024 *)
%o A147571 (Magma) [n: n in [1..2*10^4] | PrimeDivisors(n) eq [2,3,5,7]]; // _Vincenzo Librandi_, Sep 15 2015
%o A147571 (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
%Y A147571 Cf. A002473, A086780, A143207, A147572, A147573, A147574, A147575, A147576, A147577, A147578, A147579, A147580.
%K A147571 nonn
%O A147571 1,1
%A A147571 _Artur Jasinski_, Nov 07 2008