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%I #17 Aug 26 2017 02:38:13
%S 0,0,1,1,3,2,5,5,6,7,9,7,11,11,12,13,15,14,17,16,18,19,21,19,23,23,24,
%T 25,27,26,29,29,30,31,33,31,35,35,36,36,39,38,41,41,42,43,45,43,47,47
%N a(n) is the number of integers k <= n such that GCQ_A(n, k) >= 2 (see definition in comments).
%C Definition of GCQ_A: The greatest common non-divisor of type A (GCQ_A) of two positive integers a and b (a<=b) is the largest positive non-divisor q of numbers a and b such that 1<=q<=a common to a and b; GCQ_A(a, b) = 0 if no such c exists.
%C GCQ_A(1, b) = GCQ_A(2, b) = 0 for b >=1. GCQ_A(a, b) = 0 or >= 2.
%C a(n) is also the number of number k <= n such that LCQ_A(n, k) >= 2.
%C Definition of LCQ_A: The least common non-divisor of type A (LCQ_A) of two positive integers a and b (a<=b) is the least positive non-divisor q of numbers a and b such that 1<=q<=a common to a and b; LCQ_A(a, b) = 0 if no such c exists.
%C LCQ_A(1, b) = LCQ_A(2, b) = 0 for b >=1. LCQ_A(a, b) = 0 or >= 2.
%H David A. Corneth, <a href="/A196438/b196438.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n - A196437(n).
%e For n = 6, a(6) = 2 because there are 2 cases with GCQ_A(6, k) >= 2:
%e GCQ_A(6, 1) = 0, GCQ_A(6, 2) = 0, GCQ_A(6, 3) = 0, GCQ_A(6, 4) = 0, GCQ_A(6, 5) = 4, GCQ_A(6, 6) = 5.
%e Also there are 2 cases with LCQ_A(6, k) >= 2:
%e LCQ_A(6, 1) = 0, LCQ_A(6, 2) = 0, LCQ_A(6, 3) = 0, LCQ_A(6, 4) = 0, LCQ_A(6, 5) = 4, LCQ_A(6, 6) = 4.
%o (PARI) GCQ_A(a, b)=m = min(a, b); if(m < 3, return(0)); da = Set(divisors(a)); db = Set(divisors(b)); s = Set(vector(m-1,i,i)); s = setminus(s, da); s = setminus(s, db); if(#s==0,0,s[#s])
%o a(n) = sum(i=3,n,GCQ_A(i, n)>=2) \\ _David A. Corneth_, Aug 04 2017
%o (PARI) GCQ_A(a, b)=forstep(m=min(a,b)-1,2,-1, if(a%m && b%m, return(m))); 0
%o a(n) = sum(i=3,n,GCQ_A(i, n)>=2) \\ _Charles R Greathouse IV_, Aug 26 2017
%Y Cf. A196437, A196439, A196440, A196441, A196442, A196443, A196444.
%K nonn
%O 1,5
%A _Jaroslav Krizek_, Nov 26 2011
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