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A306248 Smallest m for which 2n is not m-powerful (for the definition of k-powerful see A323395). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A135732 A322584 A326154 * A327513 A327530 A084360

Adjacent sequences:  A306245 A306246 A306247 * A306249 A306250 A306251

KEYWORD

nonn,hard,more

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

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Last modified October 16 02:52 EDT 2019. Contains 328038 sequences. (Running on oeis4.)