A091414 Least number that is the sum of n positive n-th powers in at least 2 ways.

50, 251, 259, 4097, 570947, 73310705, 647282661, 79327628290, 1077347903894, 1761813250036143, 2343908545594901

Offset: 2

Author

Gabriel Cunningham (gcasey(AT)mit.edu), Mar 02 2004

Keywords

• more
• nonn

Comments

From Donovan Johnson, Sep 14 2008: (Start)

a(11) = 2^11 + 2^11 + 2^11 + 2^11 + 8^11 + 10^11 + 10^11 + 15^11 + 22^11 + 22^11 + 22^11 = 3^11 + 5^11 + 5^11 + 5^11 + 6^11 + 9^11 + 11^11 + 12^11 + 17^11 + 20^11 + 24^11.

a(12) = 2^12 + 2^12 + 2^12 + 2^12 + 2^12 + 2^12 + 2^12 + 9^12 + 9^12 + 9^12 + 15^12 + 19^12 = 3^12 + 5^12 + 5^12 + 10^12 + 10^12 + 10^12 + 10^12 + 12^12 + 12^12 + 17^12 + 17^12 + 18^12.

a(13) > 876*10^15. a(14) > 799*10^15. a(15) > 115*10^16. (End)

Examples

			a(3) = 251 because 251 = 1^3 + 5^3 + 5^3 = 2^3 + 3^3 + 6^3 and it is the smallest number that can be represented two ways as the sum of three third powers.
		

Crossrefs

a(2) = A048610(2), a(3) = A008917(1), a(4) = A185673(2). - Jonathan Sondow, Oct 24 2013

Cf. A230561, A230477.

Formula

a(n) <= A230477(n) for n > 1, with equality at least for n = 2 and inequality at least for n = 3, 4, 5. - Jonathan Sondow, Oct 24 2013

Extensions

More terms from David Wasserman, Mar 09 2006

a(11)-a(12) from Donovan Johnson, Sep 14 2008

Definition shortened by Jonathan Sondow, Oct 24 2013