OFFSET
0,2
COMMENTS
Odd prime p divides a(p-2). For n>1, a(prime(n)-2)/prime(n) = A125074(n) = {1, 29, 3343, 407889491, 298572057493, 454195874136455153, ...}. Prime p divides a((p+5)/2) for p = {19, 23, 61}. - Alexander Adamchuk, Nov 18 2006
From Mathew Englander, Jul 08 2020: (Start)
For all n != 1, a(n) mod 8 = 1.
If n mod 6 = 0, 3, or 5, then a(n) mod 6 = 1. If n mod 6 = 1, then a(n) mod 6 = 3. If n mod 6 = 2 or 4, then a(n) mod 6 = 5.
For all n, a(n)-1 is a multiple of n^2.
For n odd and n >= 3, a(n)-1 is a multiple of (n+1)^2.
For n even and n >= 0, a(n)+1 is a multiple of (n+1)^2.
For proofs, see the Englander link. (End)
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Mathew Englander, Notes on OEIS A051442
FORMULA
a(n) = (n + e + o(1)) * n^n. - Charles R Greathouse IV, Jan 12 2012
From Mathew Englander, Jul 08 2020: (Start)
a(n) = A093898(n+1, n) for n >= 1.
a(n) = a(n-1) + A258389(n) for n >= 1.
(End)
MATHEMATICA
Table[n^(n+1)+(n+1)^n, {n, 0, 20}] (* Harvey P. Dale, Oct 02 2018 *)
PROG
(PARI) a(n)=(n+1)^n+n^(n+1) \\ Charles R Greathouse IV, Jan 12 2012
(Magma)[n^(n+1)+(n+1)^n: n in [0..20]]; // Vincenzo Librandi, Jan 12 2012
(Maxima) A051442[n]:=n^(n+1)+(n+1)^n$ makelist(A051442[n], n, 0, 30); /* Martin Ettl, Oct 29 2012 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved