A374257 a(n) is the smallest number which can be represented as the sum of n distinct positive n-th powers in exactly 3 ways, or -1 if no such number exists.

-1, 325, 5104, 16578, 70211956, 201968338, 1690592199245

Offset: 1

Author

Ilya Gutkovskiy, Jul 01 2024

Keywords

• sign
• more

Examples

			a(2) = 325 = 1^2 + 18^2 = 6^2 + 17^2 = 10^2 + 15^2.
a(3) = 5104 = 1^3 + 12^3 + 15^3 = 2^3 + 10^3 + 16^3 = 9^3 + 10^3 + 15^3.
		

Crossrefs

Cf. A025304, A025401, A146756, A374227, A374256.

Programs

Python

from itertools import count
from sympy.solvers.diophantine.diophantine import power_representation
def A374257(n): return next(m for m in count(1) if len(list(power_representation(m,n,n)))==3) if n>1 else -1 # Chai Wah Wu, Jul 01 2024

Extensions

a(7) from Michael S. Branicky, Jul 09 2024