Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Mar 30 2012 19:00:25
%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