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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.

%I A359063 #17 Dec 16 2022 17:58:37
%S A359063 7,13,17,31,37,59,61,65,77,83,89,97,107,127,129,131,133,145,153,165,
%T A359063 169,179,195,197,201,221,227,235,245,249,261,269,281,293,297,303,321,
%U A359063 325,345,369,373,381,393,399,405,409,417,421,425,427,442,443,447,455,465
%N 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.
%C A359063 Inspired by former comment from _Thomas Ordowski_ in A005420.
%H A359063 Amiram Eldar, <a href="/A359063/b359063.txt">Table of n, a(n) for n = 1..68</a>
%t A359063 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 *)
%o A359063 (PARI) f(n) = vecmax(factor(2^n-1)[,1]); \\ A005420
%o A359063 isok(n) = my(x=f(2*n)); (f(n) == x) && (f(4*n) == x);
%Y A359063 Cf. A005420.
%K A359063 nonn,hard
%O A359063 1,1
%A A359063 _Michel Marcus_, Dec 15 2022
%E A359063 a(36)-a(55) from _Amiram Eldar_, Dec 15 2022