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a(n) = the sum of LCQ_A(n, k) for 1 <= k <= n (see definition in comments).
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%I #5 Mar 30 2012 19:00:25

%S 0,0,2,3,7,8,13,17,17,23,23,37,30,37,39,48,40,59,46,62,57,64,56,101,

%T 67,78,76,92,73,126,79,108,96,104,96,168,96,119,115,147

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

%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.

%e For n = 6, a(6) = 9 because 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. Sum of results is 8.

%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.: A199973 (the sum of LCQ_B(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