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A147573 Numbers with exactly 6 distinct prime divisors {2,3,5,7,11,13}.

%I A147573 #23 Feb 03 2023 09:09:27
%S A147573 30030,60060,90090,120120,150150,180180,210210,240240,270270,300300,
%T A147573 330330,360360,390390,420420,450450,480480,540540,600600,630630,
%U A147573 660660,720720,750750,780780,810810,840840,900900,960960,990990,1051050,1081080,1171170,1201200,1261260
%N A147573 Numbers with exactly 6 distinct prime divisors {2,3,5,7,11,13}.
%C A147573 Successive numbers k such that EulerPhi(x)/x = m:
%C A147573 ( Family of sequences for successive n primes )
%C A147573 m=1/2 numbers with exactly 1 distinct prime divisor {2} see A000079
%C A147573 m=1/3 numbers with exactly 2 distinct prime divisors {2,3} see A033845
%C A147573 m=4/15 numbers with exactly 3 distinct prime divisors {2,3,5} see A143207
%C A147573 m=8/35 numbers with exactly 4 distinct prime divisors {2,3,5,7} see A147571
%C A147573 m=16/77 numbers with exactly 5 distinct prime divisors {2,3,5,7,11} see A147572
%C A147573 m=192/1001 numbers with exactly 6 distinct prime divisors {2,3,5,7,11,13} see A147573
%C A147573 m=3072/17017 numbers with exactly 7 distinct prime divisors {2,3,5,7,11,13,17} see A147574
%C A147573 m=55296/323323 numbers with exactly 8 distinct prime divisors {2,3,5,7,11,13,17,19} see A147575
%C A147573 Although 39270 has exactly 6 distinct prime divisors (39270=2*3*5*7*11*17), it is not in this sequence because the 6 distinct prime divisors may only comprise 2, 3, 5, 7, 11, and 13. - _Harvey P. Dale_, Oct 11 2014
%H A147573 Amiram Eldar, <a href="/A147573/b147573.txt">Table of n, a(n) for n = 1..10000</a>
%F A147573 a(n) = 30030 * A080197(n). - _Charles R Greathouse IV_, Sep 14 2015
%F A147573 Sum_{n>=1} 1/a(n) = 1/5760. - _Amiram Eldar_, Nov 12 2020
%t A147573 a = {}; Do[If[EulerPhi[x]/x == 192/1001, AppendTo[a, x]], {x, 1, 100000}]; a
%o A147573 (PARI) is(n)=if(n%30030, return(0)); my(g=30030); while(g>1, n/=g; g=gcd(n,30030)); n==1 \\ _Charles R Greathouse IV_, Sep 14 2015
%Y A147573 Subsequence of A067885 and of A080197.
%Y A147573 Cf. A060735, A143207, A147571-A147575, A147576-A147580.
%K A147573 nonn
%O A147573 1,1
%A A147573 _Artur Jasinski_, Nov 07 2008
%E A147573 More terms from _Amiram Eldar_, Mar 10 2020