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A068191 Numbers n such that A067734(n)=0; complement of A002473; at least one prime-factor of n is larger than 7, it has 2 decimal digits.

%I A068191 #30 Sep 16 2024 14:26:10
%S A068191 11,13,17,19,22,23,26,29,31,33,34,37,38,39,41,43,44,46,47,51,52,53,55,
%T A068191 57,58,59,61,62,65,66,67,68,69,71,73,74,76,77,78,79,82,83,85,86,87,88,
%U A068191 89,91,92,93,94,95,97,99,101,102,103,104,106,107,109,110,111,113,114
%N A068191 Numbers n such that A067734(n)=0; complement of A002473; at least one prime-factor of n is larger than 7, it has 2 decimal digits.
%C A068191 Also numbers n such that A198487(n) = 0 and A107698(n) = 0. - _Jaroslav Krizek_, Nov 04 2011
%C A068191 A086299(a(n)) = 0. - _Reinhard Zumkeller_, Apr 01 2012
%C A068191 A262401(a(n)) < a(n). - _Reinhard Zumkeller_, Sep 25 2015
%C A068191 Numbers not in A007954. - _Mohammed Yaseen_, Sep 13 2022
%H A068191 Reinhard Zumkeller, <a href="/A068191/b068191.txt">Table of n, a(n) for n = 1..10000</a>
%t A068191 Select[Range@120, Last@Map[First, FactorInteger@#] > 7 &] (* _Vincenzo Librandi_, Sep 19 2016 *)
%o A068191 (Haskell)
%o A068191 import Data.List (elemIndices)
%o A068191 a068191 n = a068191_list !! (n-1)
%o A068191 a068191_list = map (+ 1) $ elemIndices 0 a086299_list
%o A068191 -- _Reinhard Zumkeller_, Apr 01 2012
%o A068191 (Python)
%o A068191 from sympy import integer_log
%o A068191 def A068191(n):
%o A068191     def f(x):
%o A068191         c = n
%o A068191         for i in range(integer_log(x,7)[0]+1):
%o A068191             i7 = 7**i
%o A068191             m = x//i7
%o A068191             for j in range(integer_log(m,5)[0]+1):
%o A068191                 j5 = 5**j
%o A068191                 r = m//j5
%o A068191                 for k in range(integer_log(r,3)[0]+1):
%o A068191                     c += (r//3**k).bit_length()
%o A068191         return c
%o A068191     m, k = n, f(n)
%o A068191     while m != k: m, k = k, f(k)
%o A068191     return m # _Chai Wah Wu_, Sep 16 2024
%Y A068191 Cf. A001222, A002473, A067734.
%Y A068191 Cf. A068183, A068184, A068185, A068186, A068187, A068189, A068190.
%Y A068191 Cf. A262401.
%K A068191 base,nonn
%O A068191 1,1
%A A068191 _Labos Elemer_, Feb 19 2002