Search: id:A084422
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%I A084422
%S A084422 1,2,4,8,12,24,28,56,72,104,116,232,248,496,544,616,728,1456,1520,3040,
%T A084422 3232,3616,3872,7744,8000,11168,11904,14656,15488,30976,31232,62464,
%U A084422 69888,76160,80256,89856,91648,183296,192640,208640,214272,428544
%N A084422 Number of subsets of integers 1 through n (including null set) containing 
               no pair of integers that share a common factor.
%D A084422 Alan Sutcliffe, Divisors and Common Factors in Sets of Integers, awaiting 
               publication.
%H A084422 N. J. Calkin and A. Granville, <a href="http://www.dms.umontreal.ca/~andrew/
               Postscript/erdosqns.ps">On the number of coprime-free sets</a>, Number 
               Theory: New York Seminar 1991-1995 (eds. D. Chudnovsky, et.al.), 
               Springer-Verlag (1996).
%e A084422 Exactly 4 of the 2^4=16 subsets of the integers from 1 through 4 contain 
               a pair of integers that share a common factor; these are {2,4}, {1,
               2,4}, {2,3,4} and {1,2,3,4}. The other 12 subsets do not; hence a(4)=12.
%Y A084422 A051026 gives the number of primitive subsets. A087080 gives the number 
               of elements in coprime subsets. A087081 gives the sum of the elements 
               in coprime subsets.
%Y A084422 Sequence in context: A027677 A103787 A032473 this_sequence A089821 A097942 
               A004653
%Y A084422 Adjacent sequences: A084419 A084420 A084421 this_sequence A084423 A084424 
               A084425
%K A084422 nonn
%O A084422 1,2
%A A084422 Matthew Vandermast (ghodges14(AT)comcast.net), Jun 26 2003
%E A084422 More terms from Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 12 2003

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