A178989 a(n) = (k^k + k!) / (k*(k + 1)), where k = prime(n) - 1.

1, 1, 14, 1128, 90942080, 57157560576, 67818988957718528, 115047995548743401472, 674758653138775267142795264, 40819609745761407890621234130376982528, 221388314080552960064314183934017536000000, 79870389582370042643423622863118514819531536385179648

Offset

1,3

Comments

According to the two theorems (Fermat and Wilson), k + 1 divides(k^k + k!) because k^k == 1 (mod k + 1) and k! == - 1 (mod k + 1) for any prime k + 1.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..50

Example

a(3) = 14 because prime(3) = 5 => p = 4 => (4^4 + 4!) / 4(4 + 1) = 280/20 = 14.

Maple

with(numtheory): for n from 1 to 20 do: p:=ithprime(n):q:=p-1:x:= (q^q + q!)/(q*p):
printf(`%d, `, x): od:

Mathematica

f[n_] := Block[{k = Prime@ n - 1}, (k^k + k!)/(k (k + 1))]; Array[f, 10] (* Robert G. Wilson v, Jan 05 2011 *)

Prog

(PARI) a(n)={my(k=prime(n)-1); (k^k + k!) / (k*(k + 1))} \\ Andrew Howroyd, Apr 13 2021

Crossrefs

Cf. A000040.

Sequence in context: A282272 A208395 A132504 * A232373 A323181 A206613

Adjacent sequences: A178986 A178987 A178988 * A178990 A178991 A178992

Keyword

nonn

Author

Michel Lagneau, Jan 03 2011

Extensions

Terms a(11) and beyond from Andrew Howroyd, Apr 13 2021

Status

approved