A359684 - OEIS

A359684

Greatest prime dividing 2^n - n for n>=2; a(1) = 1.

%I #22 Mar 30 2023 02:32:03

%S 1,2,5,3,3,29,11,31,503,13,97,1021,8179,1637,4679,13,8737,131063,

%T 524269,262139,2097131,2003,1423,2713,123817,170327,577,14983,564533,

%U 87481,318949,262657,209510599,157109,344117,2473,2255501,26861,49977801259,24481

%N Greatest prime dividing 2^n - n for n>=2; a(1) = 1.

%H Amiram Eldar, <a href="/A359684/b359684.txt">Table of n, a(n) for n = 1..429</a>

%F a(n) = A006530(A000325(n)).

%p a:= n-> max(1, numtheory[factorset](2^n-n)):

%p seq(a(n), n=1..40); # _Alois P. Heinz_, Jan 11 2023

%t a[n_] := FactorInteger[2^n - n][[-1, 1]]; Array[a, 40] (* _Amiram Eldar_, Mar 30 2023 *)

%o (PARI) a(n) = if (n==1, 1, vecmax(factor(2^n-n)[,1])); \\ _Michel Marcus_, Jan 11 2023

%o (Python)

%o from sympy import primefactors

%o def A359684(n): return 1 if n==1 else max(primefactors((1<<n)-n)) # _Chai Wah Wu_, Jan 11 2023

%Y Cf. A000040, A000325, A006530.

%K nonn

%O 1,2

%A _Philippe Deléham_, Jan 11 2023