A242875 Numbers n such that (n^n+2^2)/(n+2) is an integer.

2, 5, 8, 128, 2144, 4808, 12872, 14168, 33672, 40367, 45992, 116192, 185768, 186824, 271208, 426008, 524288, 601352, 612768, 673661, 755792, 990407, 996032, 1697607, 1878368, 2073125, 2262752, 4325960, 4810808, 6331808, 6462647, 6707352, 7527197, 7559477

Offset

1,1

Comments

Given S = (n^n+k^k)/(n+k) (here k = 2), when k = 2^m for some m > 0, there are significantly less values of n that make S an integer. For k=3, see A242883.

a(15) > 210000.

Equivalently, (-2)^n + 4 == 0 (mod n + 2). - Robert Israel, Jun 10 2014

Odd terms are A033984(2..infinity) - 2. - Robert Israel, Jun 10 2014

Links

Robert Israel, Table of n, a(n) for n = 1..100

Example

(5^5+2^2)/(5+2) = 3129/7 = 447 is an integer. Thus 5 is a member of this sequence.

Maple

filter:= proc(n) (-2)&^n + 4 mod (n+2) = 0 end proc;
select(filter, [$1..10^6]); # Robert Israel, Jun 10 2014

Prog

(PARI) for(n=1, 10^5, s=(n^n+2^2)/(n+2); if(floor(s)==s, print(n)))

Crossrefs

Cf. A242883.

Sequence in context: A264860 A061354 A162709 * A222897 A282455 A323457

Adjacent sequences: A242872 A242873 A242874 * A242876 A242877 A242878

Keyword

nonn

Author

Derek Orr, May 25 2014

Extensions

a(16)-a(34) from Robert Israel, Jun 10 2014

Status

approved