A319242 Heinz numbers of strict integer partitions of odd numbers. Squarefree numbers whose prime indices sum to an odd number.

2, 5, 6, 11, 14, 15, 17, 23, 26, 31, 33, 35, 38, 41, 42, 47, 51, 58, 59, 65, 67, 69, 73, 74, 77, 78, 83, 86, 93, 95, 97, 103, 105, 106, 109, 110, 114, 119, 122, 123, 127, 137, 141, 142, 143, 145, 149, 157, 158, 161, 167, 170, 174, 177, 178, 179, 182, 185, 191

Offset: 1

Author

Gus Wiseman, Sep 15 2018

Keywords

• nonn

Comments

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Examples

			105 is the Heinz number of (4,3,2), which is strict and has odd weight, so 105 belongs to the sequence.
The sequence of all odd-weight strict partitions begins: (1), (3), (2,1), (5), (4,1), (3,2), (7), (9), (6,1), (11), (5,2), (4,3), (8,1), (13), (4,2,1).
		

Crossrefs

Complement of the union of A319241 and A013929.

Cf. A000041, A000720, A001222, A005117, A008683, A056239, A296150, A299202, A300061, A300063.

Programs

Mathematica

Select[Range[100],And[SquareFreeQ[#],OddQ[Total[Cases[FactorInteger[#],{p_,k_}:>k*PrimePi[p]]]]]&]