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A304107 Analog for squarefree numbers when n is factored in polynomial ring GF(2)[X], so that the binary expansion of n defines the corresponding (0,1)-polynomial. These are numbers n such that the said polynomial doesn't have any duplicated irreducible divisors.

%I A304107 #21 Jul 02 2018 07:02:40
%S A304107 1,2,3,6,7,9,11,13,14,18,19,22,23,25,26,29,31,33,35,37,38,41,43,46,47,
%T A304107 49,50,53,55,58,59,61,62,66,67,70,71,73,74,77,79,82,83,86,87,89,91,93,
%U A304107 94,97,98,101,103,106,109,110,111,113,115,117,118,121,122,123,127,129,131,133,134,137,139,142,143,145,146,149,154,155,157,158,159,161
%N A304107 Analog for squarefree numbers when n is factored in polynomial ring GF(2)[X], so that the binary expansion of n defines the corresponding (0,1)-polynomial. These are numbers n such that the said polynomial doesn't have any duplicated irreducible divisors.
%C A304107 Positions of nonzeros in A091219 and A304109. Numbers n such that A091221(n) = A091222(n).
%C A304107 Numbers n that cannot be expressed as n = A048720(k,A000695(m)) for any k >= 0, m >= 2.
%C A304107 It seems that a(n) is approximately 2n for large n. See also comments in A304110.
%H A304107 Antti Karttunen, <a href="/A304107/b304107.txt">Table of n, a(n) for n = 1..32769</a>
%H A304107 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>
%F A304107 For n >= 1, A304110(a(n)) = n.
%o A304107 (PARI)
%o A304107 A304109(n) = { my(fm=factor(Pol(binary(n))*Mod(1, 2))); for(k=1, #fm~, if(fm[k, 2] > 1, return(0))); (1); };
%o A304107 k=0; n=0; while(k<100, n++; if(A304109(n), k++; print1(n,", ")));
%Y A304107 Cf. A304108 (complement), A304109 (characteristic function), A304110 (least monotonic left inverse).
%Y A304107 Cf. A000695, A014580, A048720, A091219, A091221, A091222, A304111.
%Y A304107 Cf. also A005117.
%K A304107 nonn
%O A304107 1,2
%A A304107 _Antti Karttunen_, May 13 2018