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A352490
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Nonexcedance set of A122111. Numbers k > A122111(k), where A122111 represents partition conjugation using Heinz numbers.
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16
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4, 8, 12, 16, 18, 24, 27, 32, 36, 40, 48, 50, 54, 60, 64, 72, 80, 81, 90, 96, 100, 108, 112, 120, 128, 135, 140, 144, 150, 160, 162, 168, 180, 192, 196, 200, 216, 224, 225, 240, 243, 250, 252, 256, 270, 280, 288, 300, 315, 320, 324, 336, 352, 360, 375, 378
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OFFSET
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1,1
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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 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:
4: (1,1)
8: (1,1,1)
12: (2,1,1)
16: (1,1,1,1)
18: (2,2,1)
24: (2,1,1,1)
27: (2,2,2)
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)
60: (3,2,1,1)
64: (1,1,1,1,1,1)
For example, the partition (4,4,1,1) has Heinz number 196 and its conjugate (4,2,2,2) has Heinz number 189, and 196 > 189, so 196 is in the sequence, and 189 is not.
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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 A000701.
These are the positions of positive terms in A352491.
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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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