A350029 - OEIS

A350029

Write n as n = k1 + k2 + ... + km, so that all k are distinct positive integers. a(n) is the maximum value of A001055(k1) + A001055(k2) + ... + A001055(km) over all such partitions.

1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25

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OFFSET

1,3

COMMENTS

There exist cases where a(n) < a(n-1). Some examples are n = 53, 77, 113, 125, ...

There may exist multiple partitions of n = k1 + k2 + ... + km, where a(n) = A001055(k1) + A001055(k2) + ... + A001055(km). The number of such partitions is A350032(n).

It appears that a(n) - log(A066739(n)) > 0.

If the definition of this sequence would allow k1 = k2 = km, then this sequence would be the trivial sequence a(n) = n instead.

LINKS

Table of n, a(n) for n=1..74.

Thomas Scheuerle, Examples for n = 1 to 100.

EXAMPLE

n = k1+k2+...+km A001055(k1)+...+A001055(km) = a(n)

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1 = 1 1 = 1

2 = 2 1 = 1

3 = 1 + 2 1 + 1 = 2

4 = 1 + 3 1 + 1 = 2