A147578 Numbers with exactly 5 distinct odd prime divisors {3,5,7,11,13}.

15015, 45045, 75075, 105105, 135135, 165165, 195195, 225225, 315315, 375375, 405405, 495495, 525525, 585585, 675675, 735735, 825825, 945945, 975975, 1126125, 1156155, 1216215, 1366365, 1486485, 1576575, 1756755, 1816815, 1876875, 2027025, 2147145, 2207205, 2477475

Offset: 1

Author

Artur Jasinski, Nov 07 2008

Keywords

• nonn

Comments

Numbers k such that phi(k)/k = m

( Family of sequences for successive n odd primes )

m=2/3 numbers with exactly 1 distinct prime divisor {3} see A000244;

m=8/15 numbers with exactly 2 distinct prime divisors {3,5} see A033849;

m=16/35 numbers with exactly 3 distinct prime divisors {3,5,7} see A147576;

m=32/77 numbers with exactly 4 distinct prime divisors {3,5,7,11} see A147577;

m=384/1001 numbers with exactly 5 distinct prime divisors {3,5,7,11,13} see A147578;

m=6144/17017 numbers with exactly 6 distinct prime divisors {3,5,7,11,13,17} see A147579;

m=3072/323323 numbers with exactly 7 distinct prime divisors {3,5,7,11,13,17,19} see A147580;

m=110592/323323 numbers with exactly 8 distinct prime divisors {3,5,7,11,13,17,19,23} see A147581.

Links

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

Crossrefs

Cf. A000010 (EulerPhi), A060735, A143207, A147571-A147575, A147576-A147580.

Programs

Mathematica

a = {}; Do[If[EulerPhi[x]/x == 384/1001, AppendTo[a, x]], {x, 1, 1000000}]; a

Formula

Sum_{n>=1} 1/a(n) = 1/5760. - Amiram Eldar, Dec 22 2020

Extensions

More terms from Amiram Eldar, Mar 11 2020