A135418 Number of ways of splitting the numbers from 1 to 16 into two groups so that the numbers in each group have the same sum of n-th powers.

657, 57, 1, 1

Offset

1,1

Comments

For n=1,2 there are numerous ways, while for each of n=3 and n=4 there is only one way: n=3:{1,4,6,7,10,11,13,16},{2,3,5,8,9,12,14,15} (see A133483-A133484), n=4: {1,2,3,4,8,9,10,11,12,16},{5,6,7,13,14,15}.

Presumably for n >= 5 there are no solutions.

This is true (see Fried link). - Sela Fried, Mar 17 2026

Links

Table of n, a(n) for n=1..4.

Sela Fried, Proof that A135418 is finite, 2026.

Crossrefs

Cf. A133483, A133484, A135419.

Sequence in context: A233898 A088894 A015277 * A309963 A380103 A289290

Adjacent sequences: A135415 A135416 A135417 * A135419 A135420 A135421

Keyword

nonn

Author

Zak Seidov, Dec 01 2007

Status

approved