A242885 Least number k such that (k^k+n^n)/(k+n) is an integer.

1, 2, 1, 4, 1, 3, 1, 2, 1, 5, 1, 4, 1, 14, 1, 16, 1, 3, 1, 5, 1, 10, 1, 3, 1, 6, 1, 4, 1, 4, 1, 18, 1, 17, 1, 9, 1, 26, 1, 10, 1, 6, 1, 20, 1, 7, 1, 6, 1, 8, 1, 12, 1, 10, 1, 8, 1, 3, 1, 3, 1, 6, 1, 29, 1, 6, 1, 6, 1, 5, 1, 6, 1, 17, 1, 19, 1, 12, 1, 20, 1, 5, 1, 12, 1, 42, 1

Offset

1,2

Comments

If n is odd, a(n) = 1.

a(n) <= n for all n.

a(A242901(n)) = n and a(m) <> n for m < A242901(n). - Reinhard Zumkeller, May 25 2014

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

(1^1+6^6)/(1+6) = 46657/7 is not an integer. (2^2+6^6)/(2+6) = 46660/8 = 11665/2 is not an integer. (3^3+6^6)/(3+6) = 46683/9 = 5187 is an integer. Thus a(6) = 3.

Mathematica

lnk[n_]:=Module[{k=1, n2=n^n}, While[!IntegerQ[(k^k+n2)/(k+n)], k++]; k]; Array[lnk, 90] (* or, using the lnk function defined above *) Riffle[ Table[lnk[n], {n, 2, 100, 2}], 1, {1, -1, 2}] (* Harvey P. Dale, Dec 25 2018 *)

Prog

(PARI) a(n)=for(k=1, 2500, s=(k^k+n^n)/(k+n); if(floor(s)==s, return(k)))
n=1; while(n<100, print(a(n)); n+=1)
(Haskell)
a242885 n = head [k | let nn = n ^ n,
                      k <- [1..], mod (k ^ k + nn) (k + n) == 0]
-- Reinhard Zumkeller, May 25 2014

Crossrefs

Sequence in context: A326721 A243792 A124331 * A181157 A095248 A122458

Adjacent sequences: A242882 A242883 A242884 * A242886 A242887 A242888

Keyword

nonn,look

Author

Derek Orr, May 25 2014

Status

approved