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A164296 Let S(n) be the set of all positive integers that are <= n and are coprime to n. a(n) = the number of members of S(n) that are each coprime to every other member of S(n).

%I A164296 #14 Jun 24 2024 22:27:52
%S A164296 1,1,2,2,2,2,2,4,3,2,2,4,3,4,3,4,3,6,4,6,5,4,4,8,5,5,4,6,4,8,5,8,6,6,
%T A164296 5,8,5,7,5,7,5,10,6,9,7,8,6,12,7,10,7,9,7,13,8,10,8,8,7,14,8,10,8,11,
%U A164296 8,13,8,12,9,11,9,15,10,12,10,13,10,16,10,14,11,13,10,18,11,14,10,14,10,20
%N A164296 Let S(n) be the set of all positive integers that are <= n and are coprime to n. a(n) = the number of members of S(n) that are each coprime to every other member of S(n).
%C A164296 A164296(n) + A164297(n) = phi(n) (= A000010(n) = the number of elements in S(n)).
%H A164296 Reinhard Zumkeller, <a href="/A164296/b164296.txt">Table of n, a(n) for n = 1..1000</a>
%e A164296 The positive integers that are <= 9 and are coprime to 9 are: 1,2,4,5, 7,8. 1 is coprime to each other member in S(9). While 2, 4, and 8 are non-coprime to each other. 5 is coprime to each other member of S(9). And 7 is also coprime to each other member. Since there are 3 integers in S(9) that are coprime to each other member -- these integers being 1, 5, and 7 -- then a(9) = 3.
%o A164296 (Haskell)
%o A164296 import Data.List ((\\))
%o A164296 a164296 n = length [m | let ts = a038566_row n, m <- ts,
%o A164296                         all ((== 1) . gcd m) (ts \\ [m])]
%o A164296 -- _Reinhard Zumkeller_, May 28 2015
%Y A164296 Cf. A164297.
%Y A164296 Cf. A038566, A000010.
%K A164296 nonn
%O A164296 1,3
%A A164296 _Leroy Quet_, Aug 12 2009
%E A164296 Extended by _Ray Chandler_, Mar 16 2010