A360093 a(n) is the smallest positive integer which can be represented as the sum of distinct partition numbers in exactly n ways, or -1 if no such integer exists.

1, 3, 8, 15, 18, 23, 30, 33, 38, 43, 45, 48, 56, 58, 63, 71, 74, -1, 78, 80, 85, 90, 93, 100, 101, 106, 104, 109, 113, 115, 119, 122, 130, -1, 134, 135, 145, 141, 150, 153, 146, 149, 163, 156, 158, 165, 167, 173, -1, 176, 178, 182, 181, -1, 183, 186, 196, 193, 191, 199

Offset: 1

Author

Ilya Gutkovskiy, Jan 25 2023

Keywords

• sign

Examples

			a(5) = 18 because we have [15, 3], [15, 2, 1], [11, 7], [11, 5, 2] and [7, 5, 3, 2, 1].
		

Links

• Eric Weisstein's World of Mathematics, Partition Function P, Partition Function Q

Crossrefs

Cf. A000041, A280253.