[go: up one dir, main page]

login
A077255
Numbers k such that prime(k)^k == 1 (mod k).
3
2, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 24, 27, 32, 36, 40, 42, 48, 50, 52, 54, 60, 64, 70, 72, 80, 84, 96, 100, 105, 108, 110, 114, 120, 121, 124, 125, 126, 128, 136, 144, 148, 156, 160, 162, 168, 180, 181, 182, 189, 192, 200, 210, 216, 220, 231, 234, 240, 243, 246
OFFSET
1,1
COMMENTS
Contains A023143. All terms not in A023143 are in A060679. - Robert Israel, Oct 31 2016
LINKS
FORMULA
A077254(a(n)) = 1; A077256(n) = A000040(a(n)).
EXAMPLE
prime(16)^16 mod 16 = 53^16 mod 16 = 3876269050118516845397872321 mod 16 = 1, therefore 16 is a term.
MAPLE
select(n -> ithprime(n) &^ n mod n = 1, [$1..1000]); # Robert Israel, Oct 31 2016
MATHEMATICA
Select[Range[1000], PowerMod[Prime[#], #, #] == 1&] (* Jean-François Alcover, Dec 16 2021 *)
PROG
(PARI) isok(k) = lift(Mod(prime(k), k)^k) == 1; \\ Michel Marcus, Dec 16 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 31 2002
STATUS
approved