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A259417 Even powers of the odd primes listed in increasing order. 2
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 (list; graph; refs; listen; history; text; internal format)
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:

A001248(p) = p^2,  A030514(p) = p^4,  A030516(p) = p^6,

A030629(p) = p^10, A030631(p) = p^12, A030635(p) = p^16,

A030637(p) = p^18, A137486(p) = p^22, A137492(p) = p^28,

A139571(p) = p^30, A139572(p) = p^36, A139573(p) = p^40,

A139574(p) = p^42, A139575(p) = p^46, A173533(p) = p^52,

A183062(p) = p^58, A183085(p) = p^60.

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

OEIS Wiki, Index entries for number of divisors

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

Sequence in context: A113745 A016754 A110487 * A030156 A331587 A192775

Adjacent sequences:  A259414 A259415 A259416 * A259418 A259419 A259420

KEYWORD

nonn

AUTHOR

Hartmut F. W. Hoft, Jun 26 2015

STATUS

approved

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Last modified February 28 14:16 EST 2021. Contains 341707 sequences. (Running on oeis4.)