|
|
A109473
|
|
Let m = n-th squarefree number = A005117(n), and consider the smallest pair of consecutive squarefree numbers (r,s) with gcd(r,s) = m; sequence gives values of r.
|
|
3
|
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(7) is the first unknown value.
If m (in the table in Examples) is odd then a(m) >= A020754(m-1). If m is even then a(m) >= A020754(2m-1). - Jud McCranie, Sep 30 2020
a(12) (for m=17) is greater than 3.3*10^16. - Jud McCranie, Oct 16 2020
|
|
LINKS
|
|
|
EXAMPLE
|
n | m | a(n) = r
---+----+---------------
1 | 1 | 1
2 | 2 | 422
3 | 3 | 174
4 | 5 | 22830
5 | 6 | 9216772051242
6 | 7 | 234374
7 | 10 | ?
8 | 11 | 21971536246
9 | 13 | 8678016978774
10 | 14 | ?
11 | 15 | 36442589727570
Specifically, 174 is squarefree, 177 is the next squarefree integer, and gcd(174,177) = 3; this is the first pair of consecutive squarefree numbers whose GCD is 3, so a(3)=174. - Jud McCranie, Nov 25 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,hard,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Don Reble pointed out that the value of a(5), 9216772051254, given in the DATA section should have been 9216772051242, as in the EXAMPLE section. Revised definition to clarify the difference between n and m. - N. J. A. Sloane, Nov 25 2019
|
|
STATUS
|
approved
|
|
|
|