A225944 Numbers k such that prime(k) divides k^k - 1.

1, 2, 5, 124, 181, 696, 261800, 3834909, 18836480, 51432542, 69709961, 332054520, 3140421767

Offset

1,2

Comments

a(14) > 10^12. - Giovanni Resta, May 11 2020

Links

Table of n, a(n) for n=1..13.

Mathematica

Select[Range[10^6], PowerMod[#, #, Prime@#] == 1 &] (* Giovanni Resta, May 23 2013 *)

Prog

(Python)
primes = []
n = 0
def addPrime(k):
  global n
  for p in primes:
    if k%p==0:  return
    if p*p > k:  break
  primes.append(k)
  n += 1
  if (n**n-1) % k == 0: print n,
addPrime(2)
addPrime(3)
for i in range(5, 10000000, 6):
  addPrime(i)
  addPrime(i+2)
(Python)
from sympy import nextprime, prime
from itertools import count, islice
def agen(startn=1): # generator of terms
    pn = prime(startn)
    for n in count(startn):
        if pow(n, n, pn) == 1:
            yield n
        pn = nextprime(pn)
print(list(islice(agen(), 7))) # Michael S. Branicky, May 25 2023

Crossrefs

Cf. A000040, A000312, A048861, A225945.

Sequence in context: A294513 A276109 A270481 * A270588 A214648 A175978

Adjacent sequences: A225941 A225942 A225943 * A225945 A225946 A225947

Keyword

nonn,more

Author

Alex Ratushnyak, May 21 2013

Extensions

a(8)-a(13) from Giovanni Resta, May 23 2013

Status

approved