[seqfan] Pieces of cake sequence A265286 and a question

[Neil Sloane]

Rainer R. mentioned Max Alekseyev's lovely sequence A265286.

Given n, look for the smallest set of fractions {f_1, f_2, ..., f_M} in the
range 0 to 1 such that for each k with 1 <= k <= n, we can partition the
f_i into k groups whose sums are equal. For n=5 the minimal M is 9, and a
solution is
{1/60, 1/30, 1/20, 1/12, 7/60, 2/15, 1/6, 1/5, 1/5}

OK, now look at all the solutions for a given value of n,
with M (the minimal value) parts. Now ask, what is the minimal denominator?

Is it always A003418(n) = LCM{1,2,...,n}?

If not, we get a new sequence: given n, first minimize the number of parts,
then minimize the biggest denominator

Max, do you know the answer?