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A325424 Complement of A036668: numbers not of the form 2^i*3^j*k, i + j even, (k,6) = 1.

%I A325424 #30 Feb 16 2025 08:33:58
%S A325424 2,3,8,10,12,14,15,18,21,22,26,27,32,33,34,38,39,40,46,48,50,51,56,57,
%T A325424 58,60,62,69,70,72,74,75,82,84,86,87,88,90,93,94,98,104,105,106,108,
%U A325424 110,111,118,122,123,126,128,129,130,132,134,135,136,141,142
%N A325424 Complement of A036668: numbers not of the form 2^i*3^j*k, i + j even, (k,6) = 1.
%C A325424 These are the numbers 2x and 3x as x ranges through the numbers in A036668.
%C A325424 Numbers whose squarefree part is divisible by exactly one of {2, 3}. - _Peter Munn_, Aug 24 2020
%C A325424 The asymptotic density of this sequence is 5/12. - _Amiram Eldar_, Sep 20 2020
%H A325424 Clark Kimberling, <a href="/A325424/b325424.txt">Table of n, a(n) for n = 1..10000</a>
%H A325424 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SymmetricDifference.html">Symmetric difference</a>
%F A325424 (2 * {A036668}) union (3 * {A036668}). - _Sean A. Irvine_, May 19 2019
%t A325424 a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
%t A325424 Map[MemberQ[a, #] &, Select[Flatten[{#/3, #/2}],
%t A325424 IntegerQ]]] &]], {150}]; a     (* A036668 *)
%t A325424 Complement[Range[Last[a]], a]  (* A325424 *)
%t A325424 (* _Peter J. C. Moses_, Apr 23 2019 *)
%o A325424 (Python)
%o A325424 from itertools import count
%o A325424 def A325424(n):
%o A325424     def bisection(f,kmin=0,kmax=1):
%o A325424         while f(kmax) > kmax: kmax <<= 1
%o A325424         kmin = kmax >> 1
%o A325424         while kmax-kmin > 1:
%o A325424             kmid = kmax+kmin>>1
%o A325424             if f(kmid) <= kmid:
%o A325424                 kmax = kmid
%o A325424             else:
%o A325424                 kmin = kmid
%o A325424         return kmax
%o A325424     def f(x):
%o A325424         c = n
%o A325424         for i in range(x.bit_length()+1):
%o A325424             i2 = 1<<i
%o A325424             for j in count(i&1,2):
%o A325424                 k = i2*3**j
%o A325424                 if k>x:
%o A325424                     break
%o A325424                 m = x//k
%o A325424                 c += (m-1)//6+(m-5)//6+2
%o A325424         return c
%o A325424     return bisection(f,n,n) # _Chai Wah Wu_, Jan 28 2025
%Y A325424 Cf. A325417, A036668.
%Y A325424 Symmetric difference of: A003159 and A007417; A036554 and A145204\{0}.
%K A325424 nonn,easy
%O A325424 1,1
%A A325424 _Clark Kimberling_, Apr 26 2019