cp's OEIS Frontend

A250127 Numbers k where A098550(k)/k reaches a record high.

%I A250127 #21 Jan 26 2025 09:05:13
%S A250127 1,5,7,11,13,103,177,206,684,1138,1368,1817,2046,2270,2485,4959,7411,
%T A250127 19616,22061,24482,31776,220238,314155,345422,376714,532978,1592947,
%U A250127 3707718,4235919,4763906,6874759,7929554,8984063,9511273,10038369,50020257,60003553,79962404
%N A250127 Numbers k where A098550(k)/k reaches a record high.
%e A250127 The record values of A098550(k)/k at these points are 1, 9/5, 15/7, 25/11, 35/13, 329/103, 581/177, 679/206, 3443/684, 5753/1138, 6941/1368, 9229/1817, 947/186, 11561/2270, 14963/2485, 30043/4959, 45071/7411, 120107/19616, 10399/1697, 150137/24482, 255221/31776, 1786819/220238, 2552567/314155, 2807737/345422, 3063077/376714, 4849921/532978, ...
%e A250127 The corresponding list of pairs [k, A098550(k)/k] is:
%e A250127 [1, 1], [5, 1.800000000], [7, 2.142857143], [11, 2.272727273], [13, 2.692307692], [103, 3.194174757], [177, 3.282485876], [206, 3.296116505], [684, 5.033625731], [1138, 5.055360281], [1368, 5.073830409], [1817, 5.079251513], [2046, 5.091397849], [2270, 5.092951542], [2485, 6.021327968], [4959, 6.058277879], [7411, 6.081635407], [19616, 6.122909869], [22061, 6.127872717], [24482, 6.132546361], [31776, 8.031879406], [220238, 8.113127616], [314155, 8.125183428], [345422, 8.128425520], [376714, 8.131041055], [532978, 9.099664526], ...
%e A250127 It would be nice to know what curve these points lie on.
%o A250127 (Python)
%o A250127 from math import gcd
%o A250127 A250127_list, l1, l2, s, u, l, b = [1], 3, 2, 4, 1, 1, {}
%o A250127 for n in range(4,10**4):
%o A250127     i = s
%o A250127     while True:
%o A250127         if not i in b and gcd(i,l1) == 1 and gcd(i,l2) > 1:
%o A250127             l2, l1, b[i] = l1, i, 1
%o A250127             while s in b:
%o A250127                 b.pop(s)
%o A250127                 s += 1
%o A250127             if u*n < i*l:
%o A250127                 A250127_list.append(n)
%o A250127                 u, l = i, n
%o A250127             break
%o A250127         i += 1 # _Chai Wah Wu_, Dec 06 2014
%Y A250127 Cf. A098550. See A251415 for the values of A098550 at these points.
%K A250127 nonn
%O A250127 1,2
%A A250127 _N. J. A. Sloane_, Dec 02 2014
%E A250127 a(23)-a(26) and extended example section by _Chai Wah Wu_, Dec 06 2014
%E A250127 a(27)-a(34) from _David Applegate_, Dec 18 2014
%E A250127 a(35)-a(38) from _Jinyuan Wang_, Jan 26 2025