A306248 Smallest m for which 2n is not m-powerful (for the definition of k-powerful see A323395).

1, 2, 1, 3, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 5, 1, 3, 1, 5, 1, 3, 1, 6, 1, 3, 1, 5, 1, 3, 1, 6, 1, 3, 1, 6, 1, 3, 1, 6, 1, 3, 1, 6, 1, 3, 1, 7, 1, 3, 1, 6, 1, 3, 1, 7, 1, 3, 1, 6, 1, 3, 1, 7, 1, 3, 1, 6, 1, 3, 1, 8, 1, 3, 1, 6, 1, 3, 1, 7, 1, 3, 1, 6, 1, 3, 1, 7, 1, 3, 1, 6, 1, 3, 1

Offset

1,2

Comments

This function is known as m*(2n). For odd n all values of m*(n) are 0.

Links

Table of n, a(n) for n=1..95.

S. Golan, Equal moments division of a set, Math. Comp. 77 (2008) 1695-1712.

Stan Wagon, Data for n up to 128, updated Sep 29 2019.

Example

The bipartition {1,4}, {2,3} of {1,2,3,4} has equal first power-sums. But there is no such bipartition with equal power-sums for exponents 0, 1, and 2. Therefore a(2) = 2.

Crossrefs

Cf. A323395, A323610, A323629, A323614.

Sequence in context: A356224 A364767 A326154 * A361788 A327513 A327530

Adjacent sequences: A306245 A306246 A306247 * A306249 A306250 A306251

Keyword

nonn,hard

Author

Stan Wagon, Jan 31 2019

Extensions

a(56) corrected by Stan Wagon, May 06 2019

a(72) corrected by Stan Wagon, May 24 2019

Status

approved