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A352487
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Excedance set of A122111. Numbers k < A122111(k), where A122111 represents partition conjugation using Heinz numbers.
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15
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3, 5, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94
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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 less 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:
3: (2)
5: (3)
7: (4)
10: (3,1)
11: (5)
13: (6)
14: (4,1)
15: (3,2)
17: (7)
19: (8)
21: (4,2)
22: (5,1)
23: (9)
25: (3,3)
26: (6,1)
28: (4,1,1)
For example, the partition (4,1,1) has Heinz number 28 and its conjugate (3,1,1,1) has Heinz number 40, and 28 < 40, so 28 is in the sequence, and 40 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 negative terms in A352491.
A008292 is the triangle of Eulerian numbers (version without zeros).
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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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