OFFSET
1,3
COMMENTS
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.
GCQ_A(1, b) = GCQ_A(2, b) = 0 for b >=1. GCQ_A(a, b) = 0 or >= 2.
a(n) is also the sum of number k <= n such that LCQ_A(n, k) >= 2.
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.
LCQ_A(1, b) = LCQ_A(2, b) = 0 for b >=1. LCQ_A(a, b) = 0 or >= 2.
EXAMPLE
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.
Also there are 2 same cases k with LCQ_A(6, k) >= 2: LCQ_A(6, 5) = 4, LCQ_A(6, 6) = 4.
PROG
(PARI)
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.
A196442(n) = prod(k=1, n, if(2<=GCQ_A(n, k), k, 1)); \\ Antti Karttunen, Jun 13 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Nov 26 2011
EXTENSIONS
More terms from Antti Karttunen, Jun 13 2018
STATUS
approved