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A360008
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Positions of first appearances in the sequence giving the mean of prime indices (A326567/A326568).
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10
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1, 3, 5, 6, 7, 11, 12, 13, 14, 17, 18, 19, 23, 24, 26, 29, 31, 37, 38, 41, 42, 43, 47, 48, 52, 53, 54, 58, 59, 61, 67, 71, 72, 73, 74, 76, 79, 83, 86, 89, 92, 96, 97, 101, 103, 104, 106, 107, 108, 109, 113, 122, 124, 127, 131, 137, 139, 142, 148, 149, 151, 152
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OFFSET
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1,2
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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 terms together with their prime indices begin:
1: {}
3: {2}
5: {3}
6: {1,2}
7: {4}
11: {5}
12: {1,1,2}
13: {6}
14: {1,4}
17: {7}
18: {1,2,2}
19: {8}
23: {9}
24: {1,1,1,2}
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MATHEMATICA
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nn=1000;
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
seq=Table[If[n==1, 1, Mean[prix[n]]], {n, nn}];
Select[Range[nn], FreeQ[seq[[Range[#-1]]], seq[[#]]]&]
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CROSSREFS
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A316413 lists numbers whose prime indices have integer mean.
A359908 = numbers w/ integer median of prime indices, complement A359912.
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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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