A359063 Integers k such that A005420(k) = A005420(2*k) = A005420(4*k) where A005420(k) is the largest prime factor of 2^k-1.

7, 13, 17, 31, 37, 59, 61, 65, 77, 83, 89, 97, 107, 127, 129, 131, 133, 145, 153, 165, 169, 179, 195, 197, 201, 221, 227, 235, 245, 249, 261, 269, 281, 293, 297, 303, 321, 325, 345, 369, 373, 381, 393, 399, 405, 409, 417, 421, 425, 427, 442, 443, 447, 455, 465

Offset: 1

Author

Michel Marcus, Dec 15 2022

Keywords

• nonn
• hard

Comments

Inspired by former comment from Thomas Ordowski in A005420.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..68

Crossrefs

Cf. A005420.

Programs

Mathematica

Block[{s, nn}, nn = 50; s = Map[FactorInteger[#][[-1, 1]] &, 2^Range[4 nn] - 1]; Select[Range[nn], s[[#]] == s[[2 #]] == s[[4 #]] &]] (* Michael De Vlieger, Dec 15 2022 *)

PARI

f(n) = vecmax(factor(2^n-1)[,1]); \\ A005420
isok(n) = my(x=f(2*n)); (f(n) == x) && (f(4*n) == x);

Extensions

a(36)-a(55) from Amiram Eldar, Dec 15 2022