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A319241 Heinz numbers of strict integer partitions of even numbers. Squarefree numbers whose prime indices sum to an even number. 5
1, 3, 7, 10, 13, 19, 21, 22, 29, 30, 34, 37, 39, 43, 46, 53, 55, 57, 61, 62, 66, 70, 71, 79, 82, 85, 87, 89, 91, 94, 101, 102, 107, 111, 113, 115, 118, 129, 130, 131, 133, 134, 138, 139, 146, 151, 154, 155, 159, 163, 165, 166, 173, 181, 183, 186, 187, 190, 193 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

30 is the Heinz number of (3,2,1), which is strict and has even weight, so 30 belongs to the sequence.

The sequence of all even-weight strict partitions begins: (), (2), (4), (3,1), (6), (8), (4,2), (5,1), (10), (3,2,1), (7,1), (12), (6,2), (14), (9,1), (16), (5,3), (8,2), (18), (11,1), (5,2,1), (4,3,1).

MATHEMATICA

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

CROSSREFS

Complement of the union of A319242 and A013929.

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

Sequence in context: A255607 A310185 A339620 * A310186 A289167 A289114

Adjacent sequences:  A319238 A319239 A319240 * A319242 A319243 A319244

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 15 2018

STATUS

approved

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Last modified November 27 15:36 EST 2021. Contains 349394 sequences. (Running on oeis4.)