A242883 Numbers n such that (n^n+3^3)/(n+3) is an integer.

1, 3, 5, 6, 7, 9, 15, 18, 21, 24, 27, 33, 39, 51, 58, 60, 63, 69, 75, 81, 87, 99, 105, 111, 123, 135, 153, 165, 171, 183, 186, 207, 213, 219, 231, 243, 249, 255, 267, 279, 309, 315, 351, 363, 375, 387, 393, 399, 423, 435, 453, 465, 471, 495, 501, 531, 543, 579, 603, 615, 627

Offset: 1

Author

Derek Orr, May 25 2014

Keywords

• nonn

Examples

			(5^5+3^3)/(5+3) = 3152/8 = 394 is an integer. Thus 5 is a member of this sequence.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A242875.

Programs

Magma

[n: n in [1..700] | Denominator((n^n+3^3)/(n+3))eq 1]; // Vincenzo Librandi, Apr 21 2015

Maple

A242883:=n->`if`((n^n+27) mod (n+3) = 0, n, NULL): seq(A242883(n), n=1..1000); # Wesley Ivan Hurt, Jan 10 2017

Mathematica

t[n_Integer]:=Select[Range[n], Divisible[#^# + 27, # + 3] &]; t[700] (* Vincenzo Librandi, Apr 21 2015 *)

PARI

for(n=1,1000,s=(n^n+3^3)/(n+3);if(floor(s)==s,print1(n, ", ")))