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

30030, 60060, 90090, 120120, 150150, 180180, 210210, 240240, 270270, 300300, 330330, 360360, 390390, 420420, 450450, 480480, 540540, 600600, 630630, 660660, 720720, 750750, 780780, 810810, 840840, 900900, 960960, 990990, 1051050, 1081080, 1171170, 1201200, 1261260

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

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A067885 and of A080197.

Cf. A060735, A143207, A147571-A147575, A147576-A147580.

Programs

Mathematica

a = {}; Do[If[EulerPhi[x]/x == 192/1001, AppendTo[a, x]], {x, 1, 100000}]; a

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

Formula

a(n) = 30030 * A080197(n). - Charles R Greathouse IV, Sep 14 2015

Sum_{n>=1} 1/a(n) = 1/5760. - Amiram Eldar, Nov 12 2020

Extensions

More terms from Amiram Eldar, Mar 10 2020