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Highest prime factor is greater than 3.
5

%I #32 Sep 16 2024 17:19:45

%S 5,7,10,11,13,14,15,17,19,20,21,22,23,25,26,28,29,30,31,33,34,35,37,

%T 38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,55,56,57,58,59,60,61,62,

%U 63,65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,82,83,84,85,86,87,88,89

%N Highest prime factor is greater than 3.

%C Numbers n such that A006530(n) > 3. - _Felix Fröhlich_, Dec 22 2016

%H Vincenzo Librandi, <a href="/A059485/b059485.txt">Table of n, a(n) for n = 1..9933</a>

%F a(n) ~ n. - _Charles R Greathouse IV_, Jul 06 2016

%t fQ[n_]:=! PowerMod[6, n, n]==0; Select[Range [100], fQ] (* _Vincenzo Librandi_, Dec 22 2016 *)

%o (PARI) is(n)=n>>=valuation(n,2); n/=3^valuation(n,3); n>1 \\ _Charles R Greathouse IV_, Jul 06 2016; corrected by _Michel Marcus_, May 19 2022

%o (Magma) [n: n in [1..100] | not PrimeDivisors(n) subset [2, 3]]; // _Vincenzo Librandi_, Dec 22 2016

%o (Python)

%o from sympy import integer_log

%o def A059485(n):

%o def f(x): return n+sum((x//3**i).bit_length() for i in range(integer_log(x,3)[0]+1))

%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 A003586. Cf. A007310 for numbers whose smallest prime factor (if there is one) is greater than 3.

%Y Cf. A006530.

%K nonn,easy

%O 1,1

%A Simone Caramel (simonecaramel(AT)libero.it), Feb 04 2001

%E More terms from _Henry Bottomley_, Feb 05 2001