A242870 Numbers n such that (n^n-2^2)/(n-2) is an integer.

1, 3, 4, 6, 8, 14, 20, 22, 38, 44, 56, 62, 86, 102, 110, 128, 158, 164, 182, 222, 254, 296, 302, 326, 344, 380, 422, 470, 488, 502, 542, 590, 622, 662, 686, 758, 782, 822, 884, 902, 974, 1028, 1094, 1102, 1136, 1262, 1316, 1334, 1406, 1460, 1502, 1622, 1766, 1808

Offset

1,2

Comments

a(n) is even for all n > 2. 1 and 3 are members of this sequence because (n^n-2^2)/(n-2) becomes (2^2-n^n) and (n^n-2^2), respectively, which are both integers.

Given the term (n^n-k^k)/(n-k) (here, k=2), whenever k = 2^m for some m, there are significantly fewer data values within a given range of numbers. See A242871 for k=3.

These are also numbers n such that (2^n-n^2)/(n-2) is an integer.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

(4^4-2^2)/(4-2) = 252/2 = 126 is an integer. Thus, 4 is a member of this sequence.

Maple

filter:= proc(n) (n&^n - 4) mod (n-2) = 0 end proc;
select(filter, [1, $3..1000]); # Robert Israel, May 25 2014

Mathematica

Join[{1}, Select[Range[3, 2000], IntegerQ[(#^#-4)/(#-2)]&]] (* Harvey P. Dale, Apr 24 2016 *)

Prog

(PARI) for(n=1, 2500, if(n!=2, s=(n^n-2^2)/(n-2); if(floor(s)==s, print(n))))

Crossrefs

Cf. A242871.

Sequence in context: A004713 A050475 A340770 * A025073 A325432 A204659

Adjacent sequences: A242867 A242868 A242869 * A242871 A242872 A242873

Keyword

nonn

Author

Derek Orr, May 24 2014

Status

approved