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
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
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
MATHEMATICA
a = {}; Do[If[EulerPhi[x]/x == 192/1001, AppendTo[a, x]], {x, 1, 100000}]; a
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Nov 07 2008
EXTENSIONS
More terms from Amiram Eldar, Mar 10 2020
STATUS
approved