A242870 -id:A242870 - cp's OEIS frontend

A242871 Numbers n such that (n^n-3^3)/(n-3) is an integer.

1, 2, 4, 5, 6, 7, 9, 11, 12, 15, 19, 21, 23, 27, 30, 35, 39, 42, 43, 45, 51, 57, 63, 67, 75, 81, 83, 87, 99, 103, 111, 120, 123, 129, 131, 147, 159, 163, 171, 183, 195, 203, 219, 223, 237, 243, 255, 259, 275, 291, 297, 303, 315, 323, 331, 339, 345, 354, 363, 381, 387

Offset: 1

Derek Orr, May 24 2014

nonn

These are also numbers n such that (n^3-3^n)/(n-3) is an integer.

			(5^5-3^3)/(5-3) = 3098/2 = 1549 is an integer. Thus 5 is a member of this sequence.

Robert Israel, Table of n, a(n) for n = 1..1149

Cf. A242870.

filter:= proc(n) (n^n - 27) mod (n-3) = 0 end proc:
select(filter, [1,2,$4..1000]); # Robert Israel, May 25 2014

Join[{1,2},Select[Range[4,400],IntegerQ[(#^#-27)/(#-3)]&]] (* Harvey P. Dale, Dec 17 2014 *)

for(n=1,1000,if(n!=3,s=(n^n-3^3)/(n-3);if(floor(s)==s,print(n))))

A242872 Least number k > 1 such that (k^k-n^n)/(k-n) is an integer.

Original entry on oeis.org

2, 3, 2, 2, 3, 2, 3, 2, 3, 4, 3, 3, 4, 2, 3, 4, 5, 6, 3, 2, 3, 2, 3, 4, 4, 6, 3, 4, 5, 3, 4, 8, 6, 4, 3, 4, 5, 2, 3, 4, 5, 3, 3, 2, 3, 4, 5, 6, 7, 8, 3, 4, 5, 4, 5, 2, 3, 4, 5, 5, 7, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 9, 10, 3, 4, 5, 6, 7, 8, 3, 4, 3, 4, 4, 2, 3, 4, 5, 6, 7, 8, 9, 4

Offset: 1

Derek Orr, May 24 2014

nonn

a(n) <= n-1 for n > 2 (since k > 1).

This is also the least number k such that (k^n-n^k)/(k-n) is an integer.

			(2^2-5^5)/(2-5) = 3121/3 is not an integer. (3^3-5^5)/(3-5) = 3098/2 = 1549 is an integer. Thus a(5) = 3.

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

Cf. A242870, A242871.

A242872:= proc(n)
   local nn, k;
   nn:= n^n;
   for k from 2 to n-1 do
      if (nn-k^k) mod (n-k) = 0 then return k fi
   od;
   return n+1;
end:
seq(A242872(n),n=1..100); # Robert Israel, May 25 2014

a[n_] := Switch[n, 1, 2, 2, 3, _, With[{nn = n^n}, For[k = 2, True, k++, If[Mod[nn-k^k, n-k] == 0, Return[k]]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, May 15 2023 *)

a(n)=for(k=2,n+1,if(k!=n,s=(k^k-n^n)/(k-n);if(floor(s)==s,return(k))));
n=1;while(n<100,print(a(n));n+=1)

cp's OEIS Frontend

A242871 Numbers n such that (n^n-3^3)/(n-3) is an integer.

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