|
|
A232963
|
|
Prime(m), where m is such that (sum_{i=1..m} prime(i)^14) / m is an integer.
|
|
0
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
a(8) > 1093881323023.
The primes correspond to indices n = 1, 295, 455, 4361, 10817, 132680789, 334931875, 957643538339 = A131274.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(2) = 1933, because 1193391 is the 295th prime and the sum of the first 295 primes^14 = 172657243368537051859007103457435197295421033550 when divided by 295 equals 585278791079786616471210520194695584052274690 which is an integer.
|
|
MATHEMATICA
|
t = {}; sm = 0; Do[sm = sm + Prime[n]^14; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
|
|
PROG
|
(PARI) is(n)=if(!isprime(n), return(0)); my(t=primepi(n), s); forprime(p=2, n, s+=Mod(p, t)^14); s==0 \\ Charles R Greathouse IV, Nov 30 2013
(PARI) S=n=0; forprime(p=1, , (S+=p^14)%n++||print1(p", ")) \\ M. F. Hasler, Dec 01 2013
|
|
CROSSREFS
|
Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|