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 A196444 a(n) = the smallest number m such that GCQ_A(m, k) = LCQ_A(m, k) = 0 for all 1 <= k <= n  (see definition in comments). 7

%I

%S 1,2,4,6,12,60,60,420

%N a(n) = the smallest number m such that GCQ_A(m, k) = LCQ_A(m, k) = 0 for all 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.

%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 a(5) = 12 holds: GCQ_A(12, 1) = GCQ_A(12, 2) = GCQ_A(12, 3) = GCQ_A(12, 4) = GCQ_A(12, 5) = 0.

%e Also holds: LCQ_A(12, 1) = LCQ_A(12, 2) = LCQ_A(12, 3) = LCQ_A(12, 4) = LCQ_A(12, 5) = 0.

%Y Cf. A196437, A196438, A196439, A196440, A196441, A196442, A196443.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Nov 26 2011

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Last modified September 22 00:42 EDT 2020. Contains 337276 sequences. (Running on oeis4.)