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%I #56 Oct 17 2020 02:20:17
%S 1,422,174,22830,9216772051242,234374
%N 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.
%C a(7) is the first unknown value.
%C 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
%C a(12) (for m=17) is greater than 3.3*10^16. - _Jud McCranie_, Oct 16 2020
%e n | m | a(n) = r
%e ---+----+---------------
%e 1 | 1 | 1
%e 2 | 2 | 422
%e 3 | 3 | 174
%e 4 | 5 | 22830
%e 5 | 6 | 9216772051242
%e 6 | 7 | 234374
%e 7 | 10 | ?
%e 8 | 11 | 21971536246
%e 9 | 13 | 8678016978774
%e 10 | 14 | ?
%e 11 | 15 | 36442589727570
%e 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
%Y See A109505 for another version. Cf. A005117, A051681, A020754, A337914, A337915.
%K nonn,hard,more
%O 1,2
%A _N. J. A. Sloane_, based on a suggestion from _David W. Wilson_, Aug 20 2005
%E a(5) from _Jud McCranie_, Aug 28 2005
%E a(8) from _Jud McCranie_, Aug 29 2005 (see Examples)
%E a(9) from _Jud McCranie_, Aug 31 2005 (see Examples)
%E _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
%E a(11) from _Jud McCranie_, Sep 30 2020 (see Examples)
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