

A196442


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).


8



1, 1, 3, 4, 60, 30, 2520, 6720, 45360, 604800, 19958400, 3991680, 3113510400, 14529715200, 163459296000, 3487131648000, 177843714048000, 266765571072000, 60822550204416000, 67580611338240000, 6386367771463680000, 187333454629601280000, 12926008369442488320000, 5170403347776995328000, 7755605021665492992000000, 67215243521100939264000000
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OFFSET

1,3


COMMENTS

Definition of GCQ_A: The greatest common nondivisor of type A (GCQ_A) of two positive integers a and b (a<=b) is the largest positive nondivisor 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 nondivisor of type A (LCQ_A) of two positive integers a and b (a<=b) is the least positive nondivisor 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..26.


FORMULA

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


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 PARIprogram in A196438.
A196442(n) = prod(k=1, n, if(2<=GCQ_A(n, k), k, 1)); \\ Antti Karttunen, Jun 13 2018


CROSSREFS

Cf. A196437, A196438, A196439, A196440, A196441, A196442, A196443, A196444.
Sequence in context: A331725 A067093 A041105 * A278035 A079076 A274699
Adjacent sequences: A196439 A196440 A196441 * A196443 A196444 A196445


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Nov 26 2011


EXTENSIONS

More terms from Antti Karttunen, Jun 13 2018


STATUS

approved



