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A279622 Numbers with a prime factor greater than 5.

%I A279622 #33 Sep 16 2024 17:01:44
%S A279622 7,11,13,14,17,19,21,22,23,26,28,29,31,33,34,35,37,38,39,41,42,43,44,
%T A279622 46,47,49,51,52,53,55,56,57,58,59,61,62,63,65,66,67,68,69,70,71,73,74,
%U A279622 76,77,78,79,82,83,84,85,86,87,88,89,91,92,93,94
%N A279622 Numbers with a prime factor greater than 5.
%H A279622 Vincenzo Librandi, <a href="/A279622/b279622.txt">Table of n, a(n) for n = 1..9825</a>
%F A279622 a(n) = n + O(log^3 n). - _Charles R Greathouse IV_, Dec 22 2016
%t A279622 fQ[n_]:=!PowerMod[30, n, n] == 0; Select[Range[100], fQ]
%t A279622 Select[Range[100],Max[FactorInteger[#][[;;,1]]]>5&] (* _Harvey P. Dale_, Feb 28 2023 *)
%o A279622 (PARI) isok(n) = vecmax(factor(n)[,1]) > 5; \\ _Michel Marcus_, Dec 21 2016
%o A279622 (PARI) is(n)=if(n<7, return(0)); n>>=valuation(n,2); n/=3^valuation(n,2) * 5^valuation(n,5); n>1 \\ _Charles R Greathouse IV_, Dec 22 2016
%o A279622 (Magma) [n: n in [1..100] | not PrimeDivisors(n) subset [2, 3, 5]]; // _Vincenzo Librandi_, Jan 29 2017
%o A279622 (Python)
%o A279622 from sympy import integer_log
%o A279622 def A279622(n):
%o A279622     def f(x):
%o A279622         c = n
%o A279622         for i in range(integer_log(x,5)[0]+1):
%o A279622             for j in range(integer_log(y:=x//5**i,3)[0]+1):
%o A279622                 c += (y//3**j).bit_length()
%o A279622         return c
%o A279622     m, k = n, f(n)
%o A279622     while m != k: m, k = k, f(k)
%o A279622     return m # _Chai Wah Wu_, Sep 16 2024
%Y A279622 Complement of A051037.
%Y A279622 Cf. A059485.
%K A279622 nonn,easy
%O A279622 1,1
%A A279622 _Vincenzo Librandi_, Dec 21 2016