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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.

%I A109473 #56 Oct 17 2020 02:20:17
%S A109473 1,422,174,22830,9216772051242,234374
%N 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.
%C A109473 a(7) is the first unknown value.
%C A109473 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 A109473 a(12) (for m=17) is greater than 3.3*10^16. - _Jud McCranie_, Oct 16 2020
%e A109473 n  |  m |    a(n) = r
%e A109473 ---+----+---------------
%e A109473 1  |  1 |              1
%e A109473 2  |  2 |            422
%e A109473 3  |  3 |            174
%e A109473 4  |  5 |          22830
%e A109473 5  |  6 |  9216772051242
%e A109473 6  |  7 |         234374
%e A109473 7  | 10 |              ?
%e A109473 8  | 11 |    21971536246
%e A109473 9  | 13 |  8678016978774
%e A109473 10 | 14 |              ?
%e A109473 11 | 15 | 36442589727570
%e A109473 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 A109473 See A109505 for another version. Cf. A005117, A051681, A020754, A337914, A337915.
%K A109473 nonn,hard,more
%O A109473 1,2
%A A109473 _N. J. A. Sloane_, based on a suggestion from _David W. Wilson_, Aug 20 2005
%E A109473 a(5) from _Jud McCranie_, Aug 28 2005
%E A109473 a(8) from _Jud McCranie_, Aug 29 2005 (see Examples)
%E A109473 a(9) from _Jud McCranie_, Aug 31 2005 (see Examples)
%E A109473 _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 A109473 a(11) from _Jud McCranie_, Sep 30 2020 (see Examples)