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A267117 Numbers m such that in their prime factorization m = p_1^e_1 * ... * p_k^e_k, there is no digit-position in the base-2 representation of the exponents e_1 .. e_k such that in that position all those exponents would have 1-bit.

%I A267117 #20 Sep 09 2022 04:19:22
%S A267117 1,12,18,20,28,44,45,48,50,52,60,63,68,75,76,80,84,90,92,98,99,112,
%T A267117 116,117,124,126,132,140,144,147,148,150,153,156,162,164,171,172,175,
%U A267117 176,180,188,192,198,204,207,208,212,220,228,234,236,240,242,244,245,252,260,261,268,272,275,276,279,284,288,292,294,300
%N A267117 Numbers m such that in their prime factorization m = p_1^e_1 * ... * p_k^e_k, there is no digit-position in the base-2 representation of the exponents e_1 .. e_k such that in that position all those exponents would have 1-bit.
%C A267117 The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 1, 21, 261, 2824, 29144, 294233, 2951313, 29542282, 295514868, 2955441810, 29555347819, ... . Apparently, the asymptotic density of this sequence exists and equals 0.2955... . - _Amiram Eldar_, Sep 09 2022
%H A267117 Antti Karttunen, <a href="/A267117/b267117.txt">Table of n, a(n) for n = 1..10000</a>
%e A267117 60 = 2^2 * 3^1 * 5^1 is included, as bitwise-anding together the binary representations of the exponents, "10", "01" and "01" results "00", zero.
%t A267117 {1}~Join~Select[Range@ 300, BitAnd @@ Map[Last, FactorInteger@ #] == 0 &] (* _Michael De Vlieger_, Feb 07 2016 *)
%o A267117 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A267117 (define A267117 (ZERO-POS 1 1 A267115))
%Y A267117 Indices of zeros in A267115.
%Y A267117 Cf. A054753 (subsequence), A191555 (subsequence after the initial 2).
%Y A267117 Cf. also A267114, A268376.
%K A267117 nonn,base
%O A267117 1,2
%A A267117 _Antti Karttunen_, Feb 03 2016
%E A267117 Erroneous claim corrected by _Antti Karttunen_, Feb 07 2016