

A259417


Even powers of the odd primes listed in increasing order.


4



1, 9, 25, 49, 81, 121, 169, 289, 361, 529, 625, 729, 841, 961, 1369, 1681, 1849, 2209, 2401, 2809, 3481, 3721, 4489, 5041, 5329, 6241, 6561, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 14641, 15625, 16129, 17161, 18769, 19321, 22201, 22801, 24649
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OFFSET

1,2


COMMENTS

Each of the following sequences, p^(q1) 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 odd numbers in A023194 are a subsequence of this sequence.


LINKS



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



STATUS

approved



