

A360553


Numbers > 1 whose unordered prime signature has integer median.


11



2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 46, 47, 49, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

First differs from A067340 in having 60.
A number's unordered prime signature (row n of A118914) is the multiset of positive exponents in its prime factorization.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).


LINKS



EXAMPLE

The unordered prime signature of 60 is {1,1,2}, with median 1, so 60 is in the sequence.
The unordered prime signature of 1260 is {1,1,2,2}, with median 3/2, so 1260 is not in the sequence.


MATHEMATICA

Select[Range[2, 100], IntegerQ[Median[Last/@FactorInteger[#]]]&]


CROSSREFS

Positions of even terms in A360460.
The complement is A360554 (without 1).
These partitions are counted by A360687.
A360454 = numbers whose prime indices and signature have the same median.


KEYWORD

nonn


AUTHOR



STATUS

approved



