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A363948
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Numbers whose prime indices have mean < 3/2.
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11
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2, 4, 8, 12, 16, 24, 32, 48, 64, 72, 80, 96, 128, 144, 160, 192, 256, 288, 320, 384, 432, 448, 480, 512, 576, 640, 768, 864, 896, 960, 1024, 1152, 1280, 1536, 1728, 1792, 1920, 2048, 2304, 2560, 2592, 2688, 2816, 2880, 3072, 3200, 3456, 3584, 3840, 4096, 4608
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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The initial terms, prime indices, and means:
2: {1} -> 1
4: {1,1} -> 1
8: {1,1,1} -> 1
12: {1,1,2} -> 4/3
16: {1,1,1,1} -> 1
24: {1,1,1,2} -> 5/4
32: {1,1,1,1,1} -> 1
48: {1,1,1,1,2} -> 6/5
64: {1,1,1,1,1,1} -> 1
72: {1,1,1,2,2} -> 7/5
80: {1,1,1,1,3} -> 7/5
96: {1,1,1,1,1,2} -> 7/6
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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], Mean[prix[#]]<3/2&]
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CROSSREFS
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These partitions are counted by A363947.
A360005 gives twice the median of prime indices.
A363950 ranks partitions with low mean 2, counted by A026905 redoubled.
Cf. A051293, A124944, A327473, A327476, A327482, A359889, A363727, A363942, A363943, A363946, A363951.
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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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