%I #11 Jun 13 2018 09:12:48

%S 1,1,3,4,60,30,2520,6720,45360,604800,19958400,3991680,3113510400,

%T 14529715200,163459296000,3487131648000,177843714048000,

%U 266765571072000,60822550204416000,67580611338240000,6386367771463680000,187333454629601280000,12926008369442488320000,5170403347776995328000,7755605021665492992000000,67215243521100939264000000

%N a(1) = a(2) = 1; for n >= 2, a(n) is the product of number k <= n such that GCQ_A(n, k) >= 2 (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 a(n) is also the sum of number k <= n such that LCQ_A(n, k) >= 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.

%F a(n) = A000142(n) / A196441(n).

%e For n = 6, a(6) = 30 because there are 2 cases k (k = 5, 6) with GCQ_A(6, k) >= 2: GCQ_A(6, 5) = 4, GCQ_A(6, 6) = 5 and the product of these numbers k is 30.

%e Also there are 2 same cases k with LCQ_A(6, k) >= 2: LCQ_A(6, 5) = 4, LCQ_A(6, 6) = 4.

%o (PARI)

%o GCQ_A(a, b) = { forstep(m=min(a, b)-1, 2, -1, if(a%m && b%m, return(m))); 0; }; \\ From PARI-program in A196438.

%o A196442(n) = prod(k=1,n,if(2<=GCQ_A(n,k),k,1)); \\ _Antti Karttunen_, Jun 13 2018

%Y Cf. A196437, A196438, A196439, A196440, A196441, A196442, A196443, A196444.

%K nonn

%O 1,3

%A _Jaroslav Krizek_, Nov 26 2011

%E More terms from _Antti Karttunen_, Jun 13 2018