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.

1, 422, 174, 22830, 9216772051242, 234374

Offset: 1

Author

N. J. A. Sloane, based on a suggestion from David W. Wilson, Aug 20 2005

Keywords

• nonn
• hard
• more

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

Examples

			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

See A109505 for another version. Cf. A005117, A051681, A020754, A337914, A337915.

Extensions

a(5) from Jud McCranie, Aug 28 2005

a(8) from Jud McCranie, Aug 29 2005 (see Examples)

a(9) from Jud McCranie, Aug 31 2005 (see Examples)

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

a(11) from Jud McCranie, Sep 30 2020 (see Examples)