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A199973 a(n) = the sum of LCQ_B(n, k) for 1 <= k <= n (see definition in comments). 4

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

%S 0,0,4,9,12,25,18,28,28,33,28,64,35,47,51,59,45,76,51,81,68,74,61,128,

%T 72,88,87,103,78,145,84,119,107,114,101,195,101,129,126,166

%N a(n) = the sum of LCQ_B(n, k) for 1 <= k <= n (see definition in comments).

%C Definition of LCQ_B: The least common non-divisor of type B (LCQ_B) 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<=b common to a and b; LCQ_B(a, b) = 0 if no such c exists.

%C LCQ_B(a, b) = 0 or >= 2.

%F For n = 6, a(6) = 9 because LCQ_B(6, 1) = 4, LCQ_B(6, 2) = 4, LCQ_B(6, 3) = 4, LCQ_B(6, 4) = 5, LCQ_B(6, 5) = 4, LCQ_B(6, 6) = 4. Sum of results is 25.

%Y Cf.: A196443 (the sum of GCQ_A(n, k) for 1 <= k <= n).

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

%Y Cf.: A199971 (the sum of LCQ_A(n, k) for 1 <= k <= n).

%Y Cf.: A199974 (the sum of LCQ_C(n, k) for 1 <= k <= n).

%K nonn

%O 1,3

%A _Jaroslav Krizek_, Nov 26 2011

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