Value a(6) in doubt for a = A101877

Wed Jan 16 03:33:30 CET 2008

set yields a subset {1,2,3,4,6,7} that gives reciprocal sum 1/28.
some of those missing primes there is no matching subset at all, in which
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From: hv at crypt.org
Subject: MAX(p_A093407)
Date: Wed, 16 Jan 2008 12:26:13 +0000
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  For p = prime(n), the least k such that p divides the numerator of
  a sum 1/k + 1/x1 +...+ 1/xm, where x1,...,xm (for any m) are distinct
  positive integers < k.
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From: "David W. Wilson" <wilson.d at anseri.com>
To: <seqfan at ext.jussieu.fr>
Subject: Partition-related sequence
Date: Wed, 16 Jan 2008 09:25:54 -0500
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The partition (1, 1, 2, 2) can be split into either 1, 2, or 3 subpartitions
having equal sum, to wit:

     (1, 1, 2, 2)

     (1, 2), (1, 2)

     (1, 1), (2), (2)

This is not possible for any smaller nonempty partition. If we define a(n)
as the smallest number of elements in a partition that can be split into 1
through n equal-sum subpartitions, this example shows a(3) = 4.

Can we find a few small a(n)? Is the sequence already in the OEIS?

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<p class=3DMsoNormal>The partition (1, 1, 2, 2) can be split into either 1,=
 2, or
3 subpartitions having equal sum, to wit:<o:p></o:p></p>

<p class=3DMsoNormal><o:p> </o:p></p>

<p class=3DMsoNormal>     (1, 1, 2, 2)<o:p></o:p></p>

<p class=3DMsoNormal>     (1, 2), (1, 2)<o:p></o:p></p>

<p class=3DMsoNormal>     (1, 1), (2), (2)<o:p></o:p></=
p>

<p class=3DMsoNormal><o:p> </o:p></p>

<p class=3DMsoNormal>This is not possible for any smaller nonempty partitio=
n. If
we define a(n) as the smallest number of elements in a partition that can be
split into 1 through n equal-sum subpartitions, this example shows a(3) =3D=
 4.<o:p></o:p></p>

<p class=3DMsoNormal><o:p> </o:p></p>

<p class=3DMsoNormal>Can we find a few small a(n)? Is the sequence already =
in the
OEIS?<o:p></o:p></p>

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