cp's OEIS Frontend

A147581 Numbers with exactly 8 distinct odd prime divisors {3,5,7,11,13,17,19,23}.

%I A147581 #16 Oct 23 2024 00:43:02
%S A147581 111546435,334639305,557732175,780825045,1003917915,1227010785,
%T A147581 1450103655,1673196525,1896289395,2119382265,2342475135,2565568005,
%U A147581 2788660875,3011753745,3681032355,3904125225,4350310965,5019589575,5465775315,5688868185,6135053925,6358146795
%N A147581 Numbers with exactly 8 distinct odd prime divisors {3,5,7,11,13,17,19,23}.
%C A147581 Numbers k such that phi(k)/k = m
%C A147581 ( Family of sequences for successive n odd primes )
%C A147581 m=2/3 numbers with exactly 1 distinct prime divisor {3} see A000244
%C A147581 m=8/15 numbers with exactly 2 distinct prime divisors {3,5} see A033849
%C A147581 m=16/35 numbers with exactly 3 distinct prime divisors {3,5,7} see A147576
%C A147581 m=32/77 numbers with exactly 4 distinct prime divisors {3,5,7,11} see A147577
%C A147581 m=384/1001 numbers with exactly 5 distinct prime divisors {3,5,7,11,13} see A147578
%C A147581 m=6144/17017 numbers with exactly 6 distinct prime divisors {3,5,7,11,13,17} see A147579
%C A147581 m=3072/323323 numbers with exactly 7 distinct prime divisors {3,5,7,11,13,17,19} see A147580
%C A147581 m=110592/323323 numbers with exactly 8 distinct prime divisors {3,5,7,11,13,17,19,23} see A147581
%H A147581 Amiram Eldar, <a href="/A147581/b147581.txt">Table of n, a(n) for n = 1..10000</a>
%F A147581 Sum_{n>=1} 1/a(n) = 1/36495360. - _Amiram Eldar_, Dec 22 2020
%t A147581 a = {}; Do[If[EulerPhi[111546435 x] == 36495360 x, AppendTo[a, 111546435 x]], {x, 1, 100}]; a
%o A147581 (Python)
%o A147581 from sympy import integer_log
%o A147581 def A147581(n):
%o A147581     def bisection(f,kmin=0,kmax=1):
%o A147581         while f(kmax) > kmax: kmax <<= 1
%o A147581         while kmax-kmin > 1:
%o A147581             kmid = kmax+kmin>>1
%o A147581             if f(kmid) <= kmid:
%o A147581                 kmax = kmid
%o A147581             else:
%o A147581                 kmin = kmid
%o A147581         return kmax
%o A147581     def f(x):
%o A147581         c = n+x
%o A147581         for i23 in range(integer_log(x,23)[0]+1):
%o A147581             for i19 in range(integer_log(x23:=x//23**i23,19)[0]+1):
%o A147581                 for i17 in range(integer_log(x19:=x23//19**i19,17)[0]+1):
%o A147581                     for i13 in range(integer_log(x17:=x19//17**i17,13)[0]+1):
%o A147581                         for i11 in range(integer_log(x13:=x17//13**i13,11)[0]+1):
%o A147581                             for i7 in range(integer_log(x11:=x13//11**i11,7)[0]+1):
%o A147581                                 for i5 in range(integer_log(x7:=x11//7**i7,5)[0]+1):
%o A147581                                     c -= integer_log(x7//5**i5,3)[0]+1
%o A147581         return c
%o A147581     return 111546435*bisection(f,n,n) # _Chai Wah Wu_, Oct 22 2024
%Y A147581 Cf. A060735, A143207, A147571-A147575, A147576-A147580.
%K A147581 nonn
%O A147581 1,1
%A A147581 _Artur Jasinski_, Nov 07 2008
%E A147581 More terms from _Amiram Eldar_, Mar 11 2020