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A257278 Prime powers p^m with p <= m. 5
4, 8, 16, 27, 32, 64, 81, 128, 243, 256, 512, 729, 1024, 2048, 2187, 3125, 4096, 6561, 8192, 15625, 16384, 19683, 32768, 59049, 65536, 78125, 131072, 177147, 262144, 390625, 524288, 531441, 823543, 1048576, 1594323, 1953125, 2097152, 4194304, 4782969, 5764801, 8388608, 9765625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Might be called "high" powers of primes. Motivated by challenges for which low powers of large primes provide somewhat trivial solutions, cf. A257279. The definition also avoids the question of the whether prime itself is to be considered as a prime power or not, cf. A000961 vs. A025475. In view of the condition p <= n, up to 10^10, only powers of the primes 2, 3, 5 and 7 (namely, less than 10) can occur.

a(n) = A257572(n) ^ A257573(n). - Reinhard Zumkeller, May 01 2015

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

PROG

(PARI) L=List(); lim=10; forprime(p=1, lim, for(n=p, lim*log(lim)\log(p), listput(L, p^n))); listsort(L); L

(Haskell)

import Data.Set (singleton, deleteFindMin, insert)

a257278 n = a257278_list !! (n-1)

a257278_list = f (singleton (4, 2)) 27 (tail a000040_list) where

   f s pp ps@(p:ps'@(p':_))

     | qq > pp   = pp : f (insert (pp * p, p) s) (p' ^ p') ps'

     | otherwise = qq : f (insert (qq * q, q) s') pp ps

     where ((qq, q), s') = deleteFindMin s

-- Reinhard Zumkeller, May 01 2015

CROSSREFS

Cf. A000961, A025475, A257279.

Cf. A000040, A051674 (subsequence), subsequence of A122494.

Cf. A257572, A257573.

Sequence in context: A054744 A100391 A122494 * A257279 A025197 A008371

Adjacent sequences:  A257275 A257276 A257277 * A257279 A257280 A257281

KEYWORD

nonn

AUTHOR

M. F. Hasler, Apr 28 2015

STATUS

approved

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Last modified July 24 16:44 EDT 2017. Contains 289775 sequences.