A226950 Higher powers having partitions into distinct higher powers in more than one way.

7449150177, 8936757492481, 11587386200625, 22449633661000, 30511719124992, 36443545848801, 283680450809856, 583096733580816, 613579106939841, 3958783819215057, 4098048384032001, 4556608567054336, 13469350037585841, 23887131799781376, 36604958689202176, 58634065908167841, 69952404620958561, 91953699475456000, 124976001535967232, 149272763796688896, 183001280170947121, 225430653627891712

Offset

1,1

Comments

A power m^k is called a higher power if k > 2, cf. A076467.

Links

Table of n, a(n) for n=1..22.

Reinhard Zumkeller, First 22 terms of A226950

Example

a(1) = 7449150177 = 1953^3 = 1116^3 + 279^4 = 217^4 + 1736^3;
a(2) = 8936757492481 = 1729^4 = 1729^3 + 20748^3 = 15561^3 + 17290^3;
see link for more examples and more info.

Prog

(Haskell)
import qualified Data.Set as Set (split, filter)
import Data.Set (Set, empty, size, insert, member)
a226950 n = a226950_list !! (n-1)
a226950_list = f a076467_list empty where
   f (x:xs) s | size s'' <= 1 = f xs (x `insert` s)
              | otherwise     = x : f xs (x `insert` s)
              where s'' = Set.filter ((`member` s) . (x -)) s'
                    (s', _) = Set.split (x `div` 2) s

Crossrefs

Cf. A051388, subsequence of A226777.

Sequence in context: A257899 A199632 A104851 * A225141 A015413 A288090

Adjacent sequences: A226947 A226948 A226949 * A226951 A226952 A226953

Keyword

nonn

Author

Robert Israel and Reinhard Zumkeller, Sep 13 2013

Status

approved