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Numbers with a prime factor greater than 5.
7

%I #33 Sep 16 2024 17:01:44

%S 7,11,13,14,17,19,21,22,23,26,28,29,31,33,34,35,37,38,39,41,42,43,44,

%T 46,47,49,51,52,53,55,56,57,58,59,61,62,63,65,66,67,68,69,70,71,73,74,

%U 76,77,78,79,82,83,84,85,86,87,88,89,91,92,93,94

%N Numbers with a prime factor greater than 5.

%H Vincenzo Librandi, <a href="/A279622/b279622.txt">Table of n, a(n) for n = 1..9825</a>

%F a(n) = n + O(log^3 n). - _Charles R Greathouse IV_, Dec 22 2016

%t fQ[n_]:=!PowerMod[30, n, n] == 0; Select[Range[100], fQ]

%t Select[Range[100],Max[FactorInteger[#][[;;,1]]]>5&] (* _Harvey P. Dale_, Feb 28 2023 *)

%o (PARI) isok(n) = vecmax(factor(n)[,1]) > 5; \\ _Michel Marcus_, Dec 21 2016

%o (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 (Magma) [n: n in [1..100] | not PrimeDivisors(n) subset [2, 3, 5]]; // _Vincenzo Librandi_, Jan 29 2017

%o (Python)

%o from sympy import integer_log

%o def A279622(n):

%o def f(x):

%o c = n

%o for i in range(integer_log(x,5)[0]+1):

%o for j in range(integer_log(y:=x//5**i,3)[0]+1):

%o c += (y//3**j).bit_length()

%o return c

%o m, k = n, f(n)

%o while m != k: m, k = k, f(k)

%o return m # _Chai Wah Wu_, Sep 16 2024

%Y Complement of A051037.

%Y Cf. A059485.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Dec 21 2016