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A360249
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Numbers for which the prime indices have the same median as the distinct prime indices.
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10
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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, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 100, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119, 121, 122, 123, 125, 126, 127, 128, 129, 130
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OFFSET
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1,2
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COMMENTS
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First differs from A072774 in having 90.
First differs from A242414 in having 180.
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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EXAMPLE
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The prime indices of 126 are {1,2,2,4} with median 2 and distinct prime indices {1,2,4} with median 2, so 126 is in the sequence.
The prime indices of 180 are {1,1,2,2,3} with median 2 and distinct prime indices {1,2,3} with median 2, so 180 is in the sequence.
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MAPLE
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isA360249 := proc(n)
local ifs, pidx, pe, medAll, medDist ;
if n = 1 then
return true ;
end if ;
ifs := ifactors(n)[2] ;
pidx := [] ;
for pe in ifs do
numtheory[pi](op(1, pe)) ;
pidx := [op(pidx), seq(%, i=1..op(2, pe))] ;
end do:
medAll := stats[describe, median](sort(pidx)) ;
pidx := convert(convert(pidx, set), list) ;
medDist := stats[describe, median](sort(pidx)) ;
if medAll = medDist then
true;
else
false;
end if;
end proc:
for n from 1 to 130 do
if isA360249(n) then
printf("%d, ", n) ;
end if;
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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], Median[prix[#]]==Median[Union[prix[#]]]&]
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CROSSREFS
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These partitions are counted by A360245.
The complement for mean instead of median is A360246, counted by A360242.
For multiplicities instead of distinct parts: A360454, counted by A360456.
A360005 gives median of prime indices (times two).
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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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