OFFSET
1,2
COMMENTS
Each of the following sequences, p^(q-1) with p >= 2 and q > 2 primes, except their respective first elements, powers of 2, is a subsequence:
See also the link to the OEIS Wiki.
The sequences A053182(n)^2, A065509(n)^4, A163268(n)^6 and A240693(n)^10 are subsequences of this sequence.
The odd numbers in A023194 are a subsequence of this sequence.
LINKS
Hartmut F. W. Hoft, Table of n, a(n) for n = 1..473
FORMULA
Sum_{n>=1} 1/a(n) = 1 + Sum_{k>=1} (P(2*k) - 1/2^(2*k)) = 1.21835996432366585110..., where P is the prime zeta function. - Amiram Eldar, Jul 10 2022
EXAMPLE
a(11) = 5^4 = 625 is followed by a(12) = 3^6 = 729 since no even power of an odd prime falls between them.
MATHEMATICA
a259417[bound_] := Module[{q, h, column = {}}, For[q = Prime[2], q^2 <= bound, q = NextPrime[q], For[h = 1, q^(2*h) <= bound, h++, AppendTo[column, q^(2*h)]]]; Prepend[Sort[column], 1]]
a259417[25000] (* data *)
With[{upto=25000}, Select[Union[Flatten[Table[Prime[Range[2, Floor[ Sqrt[ upto]]]]^n, {n, 0, Log[2, upto], 2}]]], #<=upto&]] (* Harvey P. Dale, Nov 25 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Hartmut F. W. Hoft, Jun 26 2015
STATUS
approved