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A363954
Numbers whose prime indices have low mean 2.
3
3, 9, 10, 14, 15, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 70, 75, 81, 84, 88, 90, 100, 104, 126, 132, 135, 136, 140, 150, 152, 156, 189, 196, 198, 204, 208, 210, 220, 225, 234, 243, 250, 252, 260, 264, 270, 272, 280, 294, 297, 300, 304, 308, 312, 315, 330, 350
OFFSET
1,1
COMMENTS
Extending the terminology of A124944, the "low mean" of a multiset is obtained by taking the mean and rounding down.
EXAMPLE
The terms together with their prime indices begin:
3: {2}
9: {2,2}
10: {1,3}
14: {1,4}
15: {2,3}
27: {2,2,2}
28: {1,1,4}
30: {1,2,3}
42: {1,2,4}
44: {1,1,5}
45: {2,2,3}
50: {1,3,3}
52: {1,1,6}
63: {2,2,4}
66: {1,2,5}
70: {1,3,4}
75: {2,3,3}
81: {2,2,2,2}
84: {1,1,2,4}
88: {1,1,1,5}
90: {1,2,2,3}
100: {1,1,3,3}
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Floor[Mean[prix[#]]]==2&]
CROSSREFS
Partitions of this type are counted by A363745.
Positions of 2's in A363943 (high A363944), triangle A363945 (high A363946).
For mean 1 we have A363949.
The high version is A363950, counted by A026905.
A112798 lists prime indices, length A001222, sum A056239.
A316413 ranks partitions with integer mean, counted by A067538.
A326567/A326568 gives mean of prime indices.
A363941 gives low median of prime indices, triangle A124943.
A363942 gives high median of prime indices, triangle A124944.
A363948 lists numbers whose prime indices have mean 1, counted by A363947.
Sequence in context: A036119 A211185 A229269 * A050852 A066887 A030608
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 05 2023
STATUS
approved