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A189716 Numbers k such that A156595(k-1) = 1; complement of A189715.

%I A189716 #19 Feb 16 2025 01:11:12
%S A189716 2,3,5,8,11,12,14,17,18,20,21,23,26,27,29,30,32,35,38,39,41,44,45,47,
%T A189716 48,50,53,56,57,59,62,65,66,68,71,72,74,75,77,80,83,84,86,89,92,93,95,
%U A189716 98,99,101,102,104,107,108,110,111,113,116,119,120,122,125,126,128,129,131,134,137,138,140,143,146,147,149,152,153,155,156,158
%N A189716 Numbers k such that A156595(k-1) = 1; complement of A189715.
%C A189716 See A156595.
%C A189716 Numbers whose squarefree part is congruent modulo 9 to 2, 3, 5 or 8. - _Peter Munn_, May 17 2020
%C A189716 The asymptotic density of this sequence is 1/2. - _Amiram Eldar_, Mar 08 2021
%H A189716 Amiram Eldar, <a href="/A189716/b189716.txt">Table of n, a(n) for n = 1..10000</a>
%t A189716 (See A189715.)
%t A189716 f[p_, e_] := (p^Mod[e, 2]); sqfpart[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[160], MemberQ[{2, 3, 5, 8}, Mod[sqfpart[#], 9]] &] (* _Amiram Eldar_, Mar 08 2021 *)
%o A189716 (Python)
%o A189716 from sympy import integer_log
%o A189716 def A189716(n):
%o A189716     def f(x): return n+x-sum(((m:=x//9**i)-2)//9+(m-5)//9+(m-8)//9+(m-3)//9+4 for i in range(integer_log(x,9)[0]+1))
%o A189716     m, k = n, f(n)
%o A189716     while m != k: m, k = k, f(k)
%o A189716     return m # _Chai Wah Wu_, Feb 15 2025
%Y A189716 Cf. A007913, A156595, A189715, A189717.
%Y A189716 Union of A055041 and A055048.
%K A189716 nonn
%O A189716 1,1
%A A189716 _Clark Kimberling_, Apr 26 2011
%E A189716 Name enhanced by _Peter Munn_, May 17 2020