A230561 Smallest number that is the sum of two positive n-th powers in >= n ways.

2, 50, 87539319

Offset

1,1

Comments

Guy, 2004: "Euler knew that 635318657 = 133^4 + 134^4 = 59^4 + 158^4, and Leech showed this to be the smallest example. No one knows of three such equal sums." Thus no one knows whether a(4) exists, which requires four such equal sums.

a(4) > 10^21 (if it exists). There is no number <= 10^21 that is the sum of two positive 4th powers in >= three ways. - Donovan Johnson, Jan 07 2014

References

R. K. Guy, Unsolved Problems in Number Theory, 3rd edition, Springer, 2004, D1.

Links

Table of n, a(n) for n=1..3.

Formula

a(n) >= A016078(n) for n > 1, with equality at least for n = 2, and inequality at least for n = 3.

Example

2 = 1^1 + 1^1.
50 = 1^2 + 7^2 = 5^2 + 5^2.
87539319 = 167^3 + 436^3 = 228^3 + 423^3 = 255^3 + 414^3.

Crossrefs

Cf. A048610, A011541 for a(2), a(3).

Cf. also A016078, A230477.

Sequence in context: A080293 A084107 A203746 * A057943 A037419 A078165

Adjacent sequences: A230558 A230559 A230560 * A230562 A230563 A230564

Keyword

hard,more,nonn,bref

Author

Jonathan Sondow, Oct 23 2013

Status

approved