A367002 a(n) is the smallest prime factor of n*2^n-1.

7, 23, 3, 3, 383, 5, 23, 17, 3, 3, 23, 5, 5, 7, 3, 3, 79, 13, 1879, 13, 3, 3, 47, 7, 229, 5, 3, 3, 32212254719, 263, 223, 5, 3, 3, 5, 73, 17, 1217, 3, 3, 6709, 29, 7, 71, 3, 3, 11, 97, 47, 228713, 3, 3, 5, 37, 5, 7, 3, 3, 9377, 11, 13, 479, 3, 3, 41, 5, 13, 137

Offset: 2

Author

Sean A. Irvine, Oct 31 2023

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 2..884 (terms 2..325 from Robert Israel)

Crossrefs

Cf. A003261, A020639, A049479, A367003, A367004, A366899.

Programs

Maple

f:= n -> min(numtheory:-factorset(n*2^n-1)):
map(f, [$2..100]); # Robert Israel, Nov 08 2023

Mathematica

Table[FactorInteger[n*2^n-1][[1,1]], {n,2,69}] (* Paul F. Marrero Romero, Dec 17 2023 *)

Formula

a(n) = A020639(A003261(n)).

a(n) = 3 iff n == 4 or 5 (mod 6). - Robert Israel, Nov 08 2023