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A352488
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Weak nonexcedance set of A122111. Numbers k >= A122111(k), where A122111 represents partition conjugation using Heinz numbers.
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13
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1, 2, 4, 6, 8, 9, 12, 16, 18, 20, 24, 27, 30, 32, 36, 40, 48, 50, 54, 56, 60, 64, 72, 75, 80, 81, 84, 90, 96, 100, 108, 112, 120, 125, 128, 135, 140, 144, 150, 160, 162, 168, 176, 180, 192, 196, 200, 210, 216, 224, 225, 240, 243, 250, 252, 256, 264, 270, 280
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OFFSET
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1,2
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COMMENTS
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The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). The sequence lists all Heinz numbers of partitions whose Heinz number is greater than or equal to that of their conjugate.
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LINKS
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FORMULA
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EXAMPLE
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The terms together with their prime indices begin:
1: ()
2: (1)
4: (1,1)
6: (2,1)
8: (1,1,1)
9: (2,2)
12: (2,1,1)
16: (1,1,1,1)
18: (2,2,1)
20: (3,1,1)
24: (2,1,1,1)
27: (2,2,2)
30: (3,2,1)
32: (1,1,1,1,1)
36: (2,2,1,1)
40: (3,1,1,1)
48: (2,1,1,1,1)
50: (3,3,1)
54: (2,2,2,1)
56: (4,1,1,1)
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Select[Range[100], #>=Times@@Prime/@conj[primeMS[#]]&]
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CROSSREFS
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These partitions are counted by A046682.
These are the positions of nonnegative terms in A352491.
A008292 is the triangle of Eulerian numbers (version without zeros).
A352525 counts compositions by weak superdiagonals, rank statistic A352517.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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