A179101 -id:A179101 - cp's OEIS frontend

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A353935 Numbers k such that a cube cannot be divided into k subcubes.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 23, 24, 25, 26, 28, 30, 31, 32, 33, 35, 37, 40, 42, 44, 47

Offset: 1

Laurence Reeves, May 11 2022

This is the finite list of 32 counts of smaller cubes that a cube cannot be subdivided into.
It is not proven that the last couple of terms belong to this sequence - see Hickerson link.
Note that cubes themselves are not on the list.

Peter Connor and Phillip Marmorino, Decomposing cubes into smaller cubes, Journal of Geometry 109 (2018), article 19.
Dean Hickerson, Further comments on A014544, Nov 01 2007 and Nov 10 2007.
Matthew Hudelson, Dissecting d-cubes into smaller d-cubes, Journal of Combinatorial Theory, Series A, 81 (1998), 190-200.

Cf. A179101 (squares).

Complement of A014544.

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