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A358526
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Numbers k whose prime indices have a different number of permutations than any number less than k.
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1
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1, 6, 12, 24, 30, 48, 60, 72, 120, 144, 180, 192, 210, 288, 360, 384, 432, 480, 576, 720, 768, 840, 864, 900, 1080, 1152, 1260, 1296, 1440, 1680, 1728, 1920, 2160, 2304, 2520, 2592, 2880, 3072, 3360, 4320, 4608, 4620, 5040, 5400, 6300, 6912, 7200, 7560, 7680
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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.
Permutations of prime indices are counted by A008480.
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
1: {}
6: {1,2}
12: {1,1,2}
24: {1,1,1,2}
30: {1,2,3}
48: {1,1,1,1,2}
60: {1,1,2,3}
72: {1,1,1,2,2}
120: {1,1,1,2,3}
144: {1,1,1,1,2,2}
180: {1,1,2,2,3}
192: {1,1,1,1,1,1,2}
210: {1,2,3,4}
288: {1,1,1,1,1,2,2}
360: {1,1,1,2,2,3}
384: {1,1,1,1,1,1,1,2}
432: {1,1,1,1,2,2,2}
480: {1,1,1,1,1,2,3}
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
fir[q_]:=Select[Range[Length[q]], !MemberQ[Take[q, #-1], q[[#]]]&];
fir[Table[Length[Permutations[primeMS[n]]], {n, 1000}]]
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CROSSREFS
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Sorted list of positions of first appearances in A008480.
A289509 lists numbers with relatively prime prime indices.
A344606 counts alternating permutations of prime indices.
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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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