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

1, 5, 7, 11, 13, 103, 177, 206, 684, 1138, 1368, 1817, 2046, 2270, 2485, 4959, 7411, 19616, 22061, 24482, 31776, 220238, 314155, 345422, 376714, 532978, 1592947, 3707718, 4235919, 4763906, 6874759, 7929554, 8984063, 9511273, 10038369, 50020257, 60003553, 79962404

Offset: 1

Author

N. J. A. Sloane, Dec 02 2014

Keywords

• nonn

Examples

			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, ...
The corresponding list of pairs [k, A098550(k)/k] is:
[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], ...
It would be nice to know what curve these points lie on.
		

Crossrefs

Cf. A098550. See A251415 for the values of A098550 at these points.

Programs

Python

from math import gcd
A250127_list, l1, l2, s, u, l, b = [1], 3, 2, 4, 1, 1, {}
for n in range(4,10**4):
    i = s
    while True:
        if not i in b and gcd(i,l1) == 1 and gcd(i,l2) > 1:
            l2, l1, b[i] = l1, i, 1
            while s in b:
                b.pop(s)
                s += 1
            if u*n < i*l:
                A250127_list.append(n)
                u, l = i, n
            break
        i += 1 # Chai Wah Wu, Dec 06 2014

Extensions

a(23)-a(26) and extended example section by Chai Wah Wu, Dec 06 2014

a(27)-a(34) from David Applegate, Dec 18 2014

a(35)-a(38) from Jinyuan Wang, Jan 26 2025