OFFSET
1,1
COMMENTS
All terms are even numbers.
EXAMPLE
4 = 2^2 (between 3 which is a prime number and 5 which is a prime number).
16 = 2^4 (between 15 = 3 * 5 and 17 which is a prime number).
32 = 2^5 (between 31 which is a prime number and 33 = 3 * 11).
36 = 2^2 * 3^2 (between 35 = 5 * 7 and 37 which is a prime number).
MAPLE
N:= 10^5:
S:= {}:
for n from 2 to isqrt(N) by 2 do
for k from 2 do
m:= n^k;
if m > N then break fi;
if numtheory:-issqrfree(m-1) and numtheory:-issqrfree(m+1) then S:= S union {m} fi
od od:
sort(convert(S, list)); # Robert Israel, May 22 2024
MATHEMATICA
Select[Range[4, 20000, 4], GCD @@ FactorInteger[#][[;; , 2]] > 1 && And @@ SquareFreeQ /@ (# + {-1, 1}) &] (* Amiram Eldar, May 22 2024 *)
PROG
(PARI) isok(k) = ispower(k) && issquarefree(k-1) && issquarefree(k+1); \\ Michel Marcus, May 22 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Massimo Kofler, May 22 2024
STATUS
approved