

A178989


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


0




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

Table of n, a(n) for n=1..10.


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:=p1: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, Jan 05 2011 *)


CROSSREFS

Sequence in context: A104226 A208395 A132504 * A232373 A206613 A198712
Adjacent sequences: A178986 A178987 A178988 * A178990 A178991 A178992


KEYWORD

nonn


AUTHOR

Michel Lagneau, Jan 03 2011


STATUS

approved



