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A319242
Heinz numbers of strict integer partitions of odd numbers. Squarefree numbers whose prime indices sum to an odd number.
6
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).
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.
Sequence in context: A002133 A092306 A349158 * A323398 A233865 A090552
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 15 2018
STATUS
approved