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A363223
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Numbers with bigomega equal to median prime index.
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2
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2, 9, 10, 50, 70, 75, 105, 110, 125, 130, 165, 170, 175, 190, 195, 230, 255, 275, 285, 290, 310, 325, 345, 370, 410, 425, 430, 435, 465, 470, 475, 530, 555, 575, 590, 610, 615, 645, 670, 686, 705, 710, 725, 730, 775, 790, 795, 830, 885, 890, 915, 925, 970
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OFFSET
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1,1
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COMMENTS
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The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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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:
2: {1}
9: {2,2}
10: {1,3}
50: {1,3,3}
70: {1,3,4}
75: {2,3,3}
105: {2,3,4}
110: {1,3,5}
125: {3,3,3}
130: {1,3,6}
165: {2,3,5}
170: {1,3,7}
175: {3,3,4}
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MATHEMATICA
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prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], PrimeOmega[#]==Median[prix[#]]&]
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CROSSREFS
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Partitions of this type are counted by A361800.
A000975 counts subsets with integer median.
A359908 lists numbers whose prime indices have integer median.
A360005 gives twice median of prime indices.
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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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