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
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10688
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
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 *)
PROG
(Magma) [n: n in [1..2*10^4] | PrimeDivisors(n) eq [2, 3, 5, 7]]; // Vincenzo Librandi, Sep 15 2015
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Nov 07 2008
STATUS
approved