A196443 - OEIS

%I #5 Mar 30 2012 19:00:25

%S 0,0,2,3,9,9,20,24,32,41,54,55,77,87,100,115,135,145,170,180,205,227,

%T 252,263,298,321,346,372,405,424,464,490,523,557,592,616,665,699,736,

%U 768,819,850,902,940,983,1031,1080,1113,1174,1219

%N  a(n) = the sum of GCQ_A(n, k) for 1 <= k <= n (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.

%e  For n = 6, a(6) = 9 because 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. Sum of results is 9.

%Y Cf. A196437, A196438, A196439, A196440, A196441, A196442, A196444, A018804.

%Y Cf. A199972 (the sum of GCQ_B(n, k) for 1<= k <= n).

%Y Cf. A199973 (the sum of LCQ_B(n, k) for 1 <= k <= n).

%K nonn

%O 1,3

%A _Jaroslav Krizek_, Nov 26 2011