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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
1, 2, 4, 6, 12, 60, 60, 420 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

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.

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

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.

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

CROSSREFS

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

Sequence in context: A081457 A261206 A127105 * A307617 A325278 A110980

Adjacent sequences:  A196441 A196442 A196443 * A196445 A196446 A196447

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Nov 26 2011

STATUS

approved

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Last modified August 4 20:00 EDT 2020. Contains 336202 sequences. (Running on oeis4.)