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

Author

Thomas Scheuerle, Dec 09 2021

Keywords

• nonn

Examples

			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.

Formula

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