A374227 -id:A374227 - cp's OEIS frontend

A374228 a(n) is the smallest number which can be represented as the sum of four distinct positive n-th powers in exactly n ways, or -1 if no such number exists.

10, 90, 1521, 300834

Offset: 1

Ilya Gutkovskiy, Jul 01 2024

			a(3) = 1521 = 1^3 + 2^3 + 8^3 + 10^3 = 1^3 + 4^3 + 5^3 + 11^3 = 4^3 + 6^3 + 8^3 + 9^3.

Cf. A025417, A025421, A146756, A374226, A374227.

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.

Original entry on oeis.org

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

Offset: 1

Ilya Gutkovskiy, Jul 01 2024

			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.

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

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

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

A374226 a(n) is the smallest number which can be represented as the sum of two distinct positive n-th powers in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

3, 65, 87539319

Offset: 1

Ilya Gutkovskiy, Jul 01 2024

			a(3) = 87539319 = 167^3 + 436^3 = 228^3 + 423^3 = 255^3 + 414^3.

Cf. A011541, A093195, A146756, A374227, A374228.

A374229 a(n) is the smallest number which can be represented as the sum of three distinct n-th powers of primes in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

10, 414, 8627527

Offset: 1

Ilya Gutkovskiy, Jul 01 2024

			a(2) = 414 = 2^2 + 7^2 + 19^2 = 2^2 + 11^2 + 17^2.

Cf. A125689, A349764, A374227, A374230.

cp's OEIS Frontend

A374228 a(n) is the smallest number which can be represented as the sum of four distinct positive n-th powers in exactly n ways, or -1 if no such number exists.

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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.

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A374226 a(n) is the smallest number which can be represented as the sum of two distinct positive n-th powers in exactly n ways, or -1 if no such number exists.

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A374229 a(n) is the smallest number which can be represented as the sum of three distinct n-th powers of primes in exactly n ways, or -1 if no such number exists.

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Author

Keywords

Examples

Crossrefs