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

1, 9, 15, 25, 35, 329, 581, 679, 3443, 5753, 6941, 9229, 10417, 11561, 14963, 30043, 45071, 120107, 135187, 150137, 255221, 1786819, 2552567, 2807737, 3063077, 4849921, 14549573, 33948953, 38798741, 43648643, 63048061, 72747599, 82447327, 87297191, 111546389

Offset: 1

Author

N. J. A. Sloane, Dec 02 2014

Keywords

• nonn

Comments

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!

Crossrefs

Cf. A098550, A241416, A250127.

Programs

Python

from math import gcd
A251415_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:
                A251415_list.append(i)
                u, l = i, n
            break
        i += 1 # Chai Wah Wu, Dec 06 2014

Extensions

a(23)-a(26) added and typo in definition corrected by Chai Wah Wu, Dec 06 2014

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

a(35) from Jinyuan Wang, Jan 26 2025