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%I #13 Nov 21 2017 03:12:04
%S 0,1,1,3,1,4,1,7,2,6,2,8,3,5,1,15,6,9,3,13,4,8,3,18,7,9,3,13,3,6,1,31,
%T 11,16,6,22,7,12,4,29,13,12,5,17,5,9,2,41,15,23,8,23,7,13,4,31,12,14,
%U 5,16,4,7,1,63,24,36,16,31,12,20,8,45,20,24,12,22
%N a(n) = number of earlier terms (with multiplicity) that have no common one bit with n in binary representation.
%C This sequence is a binary variant of A096216: here we check for common one bits and there for common prime factors.
%H Rémy Sigrist, <a href="/A295276/b295276.txt">Table of n, a(n) for n = 1..8192</a>
%H Rémy Sigrist, <a href="/A295276/a295276.png">Colored scatterplot of the first 2^15 terms</a> (where the color is function of the Hamming weight of n)
%F a(n) = #{ k such that 0 < k < n and a(k) AND n = 0 } (where AND stands for the bitwise AND operator).
%F a(2^n) = 2^n-1 for any n > 0.
%F a(2^n-1) = 1 for any n > 1.
%e The first terms, alongside the earlier terms with no common one bit with n, are:
%e n a(n) Earlier terms with no common one bit with n
%e -- ---- -------------------------------------------
%e 1 0 ()
%e 2 1 (0)
%e 3 1 (0)
%e 4 3 (0, 1, 1)
%e 5 1 (0)
%e 6 4 (0, 1, 1, 1)
%e 7 1 (0)
%e 8 7 (0, 1, 1, 3, 1, 4, 1)
%e 9 2 (0, 4)
%e 10 6 (0, 1, 1, 1, 4, 1)
%e 11 2 (0, 4)
%e 12 8 (0, 1, 1, 3, 1, 1, 2, 2)
%e 13 3 (0, 2, 2)
%e 14 5 (0, 1, 1, 1, 1)
%e 15 1 (0)
%e 16 15 (0, 1, 1, 3, 1, 4, 1, 7, 2, 6, 2, 8, 3, 5, 1)
%e 17 6 (0, 4, 2, 6, 2, 8)
%e 18 9 (0, 1, 1, 1, 4, 1, 8, 5, 1)
%e 19 3 (0, 4, 8)
%e 20 13 (0, 1, 1, 3, 1, 1, 2, 2, 8, 3, 1, 9, 3)
%o (PARI) a = vector(76); for(n=1, #a, a[n] = sum(i=1, n-1, bitand(a[i],n)==0); print1(a[n] ", "))
%Y Cf. A096216.
%K nonn,base
%O 1,4
%A _Rémy Sigrist_, Nov 19 2017