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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
OFFSET
1,2
COMMENTS
This function is known as m*(2n). For odd n all values of m*(n) are 0.
LINKS
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
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