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A147577 Numbers with exactly 4 distinct odd prime divisors {3,5,7,11}.

%I A147577 #16 Oct 22 2024 20:17:07
%S A147577 1155,3465,5775,8085,10395,12705,17325,24255,28875,31185,38115,40425,
%T A147577 51975,56595,63525,72765,86625,88935,93555,114345,121275,139755,
%U A147577 144375,155925,169785,190575,202125,218295,259875,266805,280665,282975,317625
%N A147577 Numbers with exactly 4 distinct odd prime divisors {3,5,7,11}.
%C A147577 Numbers k such that phi(k)/k = m
%C A147577 ( Family of sequences for successive n odd primes )
%C A147577 m=2/3 numbers with exactly 1 distinct prime divisor {3} see A000244
%C A147577 m=8/15 numbers with exactly 2 distinct prime divisors {3,5} see A033849
%C A147577 m=16/35 numbers with exactly 3 distinct prime divisors {3,5,7} see A147576
%C A147577 m=32/77 numbers with exactly 4 distinct prime divisors {3,5,7,11} see A147577
%C A147577 m=384/1001 numbers with exactly 5 distinct prime divisors {3,5,7,11,13} see A147578
%C A147577 m=6144/17017 numbers with exactly 6 distinct prime divisors {3,5,7,11,13,17} see A147579
%C A147577 m=3072/323323 numbers with exactly 7 distinct prime divisors {3,5,7,11,13,17,19} see A147580
%C A147577 m=110592/323323 numbers with exactly 8 distinct prime divisors {3,5,7,11,13,17,19,23} see A147581
%H A147577 Amiram Eldar, <a href="/A147577/b147577.txt">Table of n, a(n) for n = 1..10000</a>
%F A147577 Sum_{n>=1} 1/a(n) = 1/480. - _Amiram Eldar_, Dec 22 2020
%t A147577 a = {}; Do[If[EulerPhi[x]/x == 32/77, AppendTo[a, x]], {x, 1, 1000000}]; a
%t A147577 Select[Range[350000],EulerPhi[#]/#==32/77&] (* _Harvey P. Dale_, Mar 25 2016 *)
%o A147577 (Python)
%o A147577 from sympy import integer_log
%o A147577 def A147577(n):
%o A147577     def bisection(f,kmin=0,kmax=1):
%o A147577         while f(kmax) > kmax: kmax <<= 1
%o A147577         while kmax-kmin > 1:
%o A147577             kmid = kmax+kmin>>1
%o A147577             if f(kmid) <= kmid:
%o A147577                 kmax = kmid
%o A147577             else:
%o A147577                 kmin = kmid
%o A147577         return kmax
%o A147577     def f(x):
%o A147577         c = n+x
%o A147577         for i11 in range(integer_log(x,11)[0]+1):
%o A147577             for i7 in range(integer_log(x11:=x//11**i11,7)[0]+1):
%o A147577                 for i5 in range(integer_log(x7:=x11//7**i7,5)[0]+1):
%o A147577                     c -= integer_log(x7//5**i5,3)[0]+1
%o A147577         return c
%o A147577     return 1155*bisection(f,n,n) # _Chai Wah Wu_, Oct 22 2024
%Y A147577 Cf. A060735, A143207, A147571-A147575, A147576-A147580.
%K A147577 nonn
%O A147577 1,1
%A A147577 _Artur Jasinski_, Nov 07 2008