

A362050


Numbers whose prime indices satisfy: (length) = 2*(median).


5



4, 54, 81, 90, 100, 126, 135, 140, 189, 198, 220, 234, 260, 297, 306, 340, 342, 351, 380, 414, 459, 460, 513, 522, 558, 580, 620, 621, 666, 738, 740, 774, 783, 820, 837, 846, 860, 940, 954, 999, 1060, 1062, 1098, 1107, 1161, 1180, 1206, 1220, 1269, 1278, 1314
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OFFSET

1,1


COMMENTS

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).
All terms are squarefree.


LINKS



EXAMPLE

The terms together with their prime indices begin:
4: {1,1}
54: {1,2,2,2}
81: {2,2,2,2}
90: {1,2,2,3}
100: {1,1,3,3}
126: {1,2,2,4}
135: {2,2,2,3}
140: {1,1,3,4}
189: {2,2,2,4}
198: {1,2,2,5}


MATHEMATICA

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], PrimeOmega[#]==2*Median[prix[#]]&]


CROSSREFS

Before multiplying the median by 2, A361800 counts partitions of this type.
Partitions of this type are counted by A362049.


KEYWORD

nonn


AUTHOR



STATUS

approved



