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A359889
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Numbers that are 1 or whose prime indices have the same mean as median.
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47
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 67, 69, 71, 73, 74, 77, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94
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OFFSET
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1,2
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COMMENTS
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First differs from A236510 in having 252 (prime indices {1,1,2,2,4}).
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.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
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LINKS
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FORMULA
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EXAMPLE
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The prime indices of 900 are {1,1,2,2,3,3}, with mean 2 and median 2, so 900 is in the sequence.
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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[100], #==1||Mean[prix[#]]==Median[prix[#]]&]
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CROSSREFS
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The RHS (median of prime indices) is A360005/2.
A316413 lists numbers whose prime indices have integer mean.
A359908 lists numbers whose prime indices have integer median.
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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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