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

1,1

Comments

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

Links

Table of n, a(n) for n=1..59.

Example

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).

Mathematica

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

Crossrefs

Complement of the union of A319241 and A013929.

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

Sequence in context: A002133 A092306 A349158 * A323398 A233865 A090552

Adjacent sequences: A319239 A319240 A319241 * A319243 A319244 A319245

Keyword

nonn

Author

Gus Wiseman, Sep 15 2018

Status

approved