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 A230563 Smallest number that is the sum of three positive n-th powers in more than one way. 1

%I

%S 5,27,251,2673,1375298099,160426514

%N Smallest number that is the sum of three positive n-th powers in more than one way.

%C a(7) > 10^26 (if it exists). - _Donovan Johnson_, Nov 22 2013

%C From _Duncan Moore_, Oct 07 2017: (Start)

%C This sequence is the correct version of A046093.

%C a(7) > 33055^7 ~ 4.31*10^31 (if it exists). (End)

%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, section 21.11.

%e 5 = 1^1 + 1^1 + 3^1 = 1^1 + 2^1 + 2^1.

%e 27 = 1^2 + 1^2 + 5^2 = 3^2 + 3^2 + 3^2.

%e 251 = 1^3 + 5^3 + 5^3 = 2^3 + 3^3 + 6^3.

%e 2673 = 2^4 + 4^4 + 7^4 = 3^4 + 6^4 + 6^4.

%e 1375298099 = 3^5 + 54^5 + 62^5 = 24^5 + 28^5 + 67^5.

%e 160426514 = 3^6 + 19^6 + 22^6 = 10^6 + 15^6 + 23^6.

%Y Cf. A046093, A230477, A230561, A230562.

%K hard,more,nonn

%O 1,1

%A _Jonathan Sondow_, Oct 25 2013

%E a(4) and a(5) corrected by _Donovan Johnson_, Oct 28 2013

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Last modified June 1 19:32 EDT 2020. Contains 334762 sequences. (Running on oeis4.)