A350032 Write n as n = k1 + k2 + ... + km, so that all k are distinct positive integers and b = A001055(k1) + A001055(k2) + ... + A001055(km) becomes maximal. a(n) is the number of such partitions which attain this maximum.

1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 2, 5, 2, 3, 1, 2, 3, 1, 2, 4, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 5, 1, 2, 4, 1, 1, 3, 7, 1, 3, 6, 1, 2, 5, 1, 1, 4, 1, 1, 3, 1, 11, 2, 4, 9, 2, 3, 7, 1, 2, 4, 7, 1, 3, 6, 1, 2, 4, 1, 1, 3, 1, 1, 2, 1, 6, 1, 2, 4, 1, 1, 3, 3, 1, 1, 1, 5, 5, 1

Offset

1,4

Links

Table of n, a(n) for n=1..90.

Formula

a(n) <= 1 + A066739(n) - A000041(n).

Example

a(6) = 2:
6 = 1 + 2 + 3 and A001055(1) + A001055(2) + A001055(3) = 3;
6 = 2 + 4     and A001055(2) + A001055(4) = 3.

Crossrefs

Cf. A000009, A000041, A066739, A001055, A350029.

Sequence in context: A326625 A188884 A116679 * A379062 A146290 A347045

Adjacent sequences: A350029 A350030 A350031 * A350033 A350034 A350035

Keyword

nonn

Author

Thomas Scheuerle, Dec 09 2021

Status

approved