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A375702
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Length of the n-th maximal run of adjacent (increasing by one at a time) non-perfect-powers.
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3
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2, 3, 6, 8, 1, 4, 3, 12, 14, 16, 18, 20, 3, 2, 15, 24, 26, 19, 8, 17, 12, 32, 34, 18, 17, 38, 40, 42, 27, 16, 46, 48, 50, 52, 54, 56, 58, 60, 38, 23, 64, 66, 68, 70, 34, 37, 74, 76, 78, 80, 46, 35, 84, 86, 88, 22, 67, 70, 9, 11, 94, 96, 98, 100, 102, 39, 64
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OFFSET
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1,1
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COMMENTS
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Non-perfect-powers A007916 are numbers with no proper integer roots.
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LINKS
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FORMULA
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For n > 2 we have a(n) = A053289(n+1) - 1.
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EXAMPLE
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The list of all non-perfect-powers, split into runs, begins:
2 3
5 6 7
10 11 12 13 14 15
17 18 19 20 21 22 23 24
26
28 29 30 31
33 34 35
37 38 39 40 41 42 43 44 45 46 47 48
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MATHEMATICA
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radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
Length/@Split[Select[Range[100], radQ], #1+1==#2&]//Most
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CROSSREFS
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For runs of non-perfect-powers (A007916):
A046933 counts composite numbers between primes.
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KEYWORD
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nonn,new
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AUTHOR
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STATUS
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approved
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