A147575 Numbers with exactly 8 distinct prime divisors {2,3,5,7,11,13,17,19}.

9699690, 19399380, 29099070, 38798760, 48498450, 58198140, 67897830, 77597520, 87297210, 96996900, 106696590, 116396280, 126095970, 135795660, 145495350, 155195040, 164894730, 174594420, 184294110, 193993800, 203693490, 213393180, 232792560, 242492250, 252191940

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

Links

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

Crossrefs

Cf. A060735, A080682, A143207, A147571-A147575, A147576-A147580.

Programs

Mathematica

a = {}; Do[If[EulerPhi[9699690 x] == 1658880 x, AppendTo[a, 9699690 x]], {x, 1, 100}]; a

Formula

a(n) = 9699690 * A080682(n). - Amiram Eldar, Mar 10 2020

Sum_{n>=1} 1/a(n) = 1/1658880. - Amiram Eldar, Nov 12 2020

Extensions

More terms from Amiram Eldar, Mar 10 2020