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A251415 Values of A098550 where A098550(k)/k reaches a record high.

%I A251415 #19 Jan 26 2025 09:05:19
%S A251415 1,9,15,25,35,329,581,679,3443,5753,6941,9229,10417,11561,14963,30043,
%T A251415 45071,120107,135187,150137,255221,1786819,2552567,2807737,3063077,
%U A251415 4849921,14549573,33948953,38798741,43648643,63048061,72747599,82447327,87297191,111546389
%N A251415 Values of A098550 where A098550(k)/k reaches a record high.
%C A251415 The prime factorizations of these numbers are 1, 3^2, 3*5, 5^2, 5*7, 7*47, 7*83, 7*97, 11*313, 11*523, 11*631, 11*839, 11*947, 11*1051, 13*1151, 13*2311, 13*3467, 13*9239, 13*10399, 13*11549, 17*15013, 17*105107, ... It would be nice to know what this is trying to tell us!
%o A251415 (Python)
%o A251415 from math import gcd
%o A251415 A251415_list, l1, l2, s, u, l, b = [1], 3, 2, 4, 1, 1, {}
%o A251415 for n in range(4,10**4):
%o A251415     i = s
%o A251415     while True:
%o A251415         if not i in b and gcd(i,l1) == 1 and gcd(i,l2) > 1:
%o A251415             l2, l1, b[i] = l1, i, 1
%o A251415             while s in b:
%o A251415                 b.pop(s)
%o A251415                 s += 1
%o A251415             if u*n < i*l:
%o A251415                 A251415_list.append(i)
%o A251415                 u, l = i, n
%o A251415             break
%o A251415         i += 1 # _Chai Wah Wu_, Dec 06 2014
%Y A251415 Cf. A098550, A241416, A250127.
%K A251415 nonn
%O A251415 1,2
%A A251415 _N. J. A. Sloane_, Dec 02 2014
%E A251415 a(23)-a(26) added and typo in definition corrected by _Chai Wah Wu_, Dec 06 2014
%E A251415 a(27)-a(34) from _David Applegate_, Dec 18 2014
%E A251415 a(35) from _Jinyuan Wang_, Jan 26 2025