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A334104 Numbers m for which A329697(m) = 4.

%I A334104 #19 Jun 05 2020 16:30:46
%S A334104 43,47,49,57,59,63,67,69,71,77,79,81,86,87,91,93,94,95,98,99,105,107,
%T A334104 109,111,114,115,117,118,121,126,131,134,135,138,142,143,145,149,151,
%U A334104 154,155,157,158,159,162,165,167,169,172,174,175,179,181,182,183,185,186,188,190,195,196,198,210,214,218,219,222,225
%N A334104 Numbers m for which A329697(m) = 4.
%C A334104 Squares of A334102 form a subsequence.
%C A334104 Among the first 12193 terms (terms < 2^31), there are terms with binary weights 2 - 16, except no terms with weight 13, 14 or 15. For example, 1025 is the first term with binary weight 2, and 65535 is the first term with binary weight 16.
%H A334104 Antti Karttunen, <a href="/A334104/b334104.txt">Table of n, a(n) for n = 1..12193; all terms <= 2^31</a>
%e A334104 63 = 7*9 is a term as both 7 and 9 are terms of A334102.
%e A334104 65535 = 3*5*17*257 is a term as it is a product of four Fermat primes, thus in four steps all odd primes can be eliminated with p -> (p-1) map.
%t A334104 Position[Array[Length@NestWhileList[# - #/FactorInteger[#][[-1, 1]] &, #, # != 2^IntegerExponent[#, 2] &] - 1 &, 225], 4][[All, 1]] (* _Michael De Vlieger_, Apr 30 2020 *)
%o A334104 (PARI)
%o A334104 A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
%o A334104 isA334104(n) = (4==A329697(n));
%Y A334104 Row 4 of A334100.
%Y A334104 Cf. A052126, A171462, A209229, A329697, A334101, A334102, A334103, A334105, A334106.
%Y A334104 Cf. A334094 (primes present).
%K A334104 nonn
%O A334104 1,1
%A A334104 _Antti Karttunen_, Apr 14 2020