%I #18 Nov 12 2020 10:34:56

%S 510510,1021020,1531530,2042040,2552550,3063060,3573570,4084080,

%T 4594590,5105100,5615610,6126120,6636630,7147140,7657650,8168160,

%U 8678670,9189180,10210200,10720710,11231220,12252240,12762750,13273260,13783770

%N Numbers with exactly 7 distinct prime divisors {2,3,5,7,11,13,17}.

%C Successive numbers k such that EulerPhi(x)/x = m:

%C ( Family of sequences for successive n primes )

%C m=1/2 numbers with exactly 1 distinct prime divisor {2} see A000079

%C m=1/3 numbers with exactly 2 distinct prime divisors {2,3} see A033845

%C m=4/15 numbers with exactly 3 distinct prime divisors {2,3,5} see A143207

%C m=8/35 numbers with exactly 4 distinct prime divisors {2,3,5,7} see A147571

%C m=16/77 numbers with exactly 5 distinct prime divisors {2,3,5,7,11} see A147572

%C m=192/1001 numbers with exactly 6 distinct prime divisors {2,3,5,7,11,13} see A147573

%C m=3072/17017 numbers with exactly 7 distinct prime divisors {2,3,5,7,11,13,17} see A147574

%C m=55296/323323 numbers with exactly 8 distinct prime divisors {2,3,5,7,11,13,17,19} see A147575

%H Amiram Eldar, <a href="/A147574/b147574.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)

%F a(n) = 510510 * A080681(n). - _Amiram Eldar_, Mar 10 2020

%F Sum_{n>=1} 1/a(n) = 1/92160. - _Amiram Eldar_, Nov 12 2020

%t a = {}; Do[If[EulerPhi[x 510510] == 92160 x, AppendTo[a, 510510 x]], {x, 1, 100}]; a

%t sdpdQ[n_]:=Module[{f=FactorInteger[n][[All,1]]},Length[f]==7&&Max[f]==17]; Select[Range[510510,138*10^5,510510],sdpdQ] (* _Harvey P. Dale_, Aug 03 2019 *)

%Y Cf. A060735, A080681, A143207, A147571-A147575, A147576-A147580.

%K nonn

%O 1,1

%A _Artur Jasinski_, Nov 07 2008