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 A242875 Numbers n such that (n^n+2^2)/(n+2) is an integer. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified June 24 18:46 EDT 2021. Contains 345419 sequences. (Running on oeis4.)