OFFSET
1,1
COMMENTS
365000 < a(19) <= 1048576; a(20) = 1000; a(21) = 4096; a(22) = 43541. - Daniel Suteu, Jul 10 2022
EXAMPLE
a(3) = 7 is the smallest number of the set {k(i)} = {7, 9, 13, 15, 19, 21, ...} where k(i)^3 - 1 contains 3 distinct prime divisors.
MAPLE
with(numtheory) :for n from 1 to 10 do:ii:=0:for k from 1 to 10^10 while(ii=0) do:x:=k^n-1:y:=factorset(x):n1:=nops(y):if n1=n then ii:=1: printf ( "%d %d \n", n, k):
else fi:od:od:
MATHEMATICA
L = {}; Do[n = 1; While[Length[FactorInteger[n^k - 1]] != k, n++]; Print@AppendTo[L, n], {k, 15}] (* Giovanni Resta, Nov 10 2012 *)
PROG
(PARI) a(n) = my(k=2); while (omega(k^n-1) != n, k++); k; \\ Daniel Suteu, Jul 10 2022
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Michel Lagneau, Nov 09 2012
EXTENSIONS
a(13)-a(18), a(20)-a(22) from Daniel Suteu, Jul 10 2022
a(19) from Jinyuan Wang, Feb 13 2023
STATUS
approved