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A375702
Length of the n-th maximal run of adjacent (increasing by one at a time) non-perfect-powers.
16
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
OFFSET
1,1
COMMENTS
Non-perfect-powers A007916 are numbers with no proper integer roots.
FORMULA
For n > 2 we have a(n) = A053289(n+1) - 1.
EXAMPLE
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
Row n has length a(n), first A375703, last A375704, sum A375705.
MATHEMATICA
radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
Length/@Split[Select[Range[100], radQ], #1+1==#2&]//Most
CROSSREFS
For nonsquarefree numbers we have A053797, anti-runs A373409.
For squarefree numbers we have A120992, anti-runs A373127.
For nonprime numbers we have A176246, anti-runs A373403.
For prime-powers we have A373675, anti-runs A373576.
For non-prime-powers we have A373678, anti-runs A373679.
The anti-run version is A375736, sum A375737.
For runs of non-perfect-powers (A007916):
- length: A375702 (this).
- first: A375703
- last: A375704
- sum: A375705
A001597 lists perfect-powers, differences A053289.
A007916 lists non-perfect-powers, differences A375706.
A046933 counts composite numbers between primes.
Sequence in context: A291659 A302090 A088414 * A133441 A086254 A265297
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 27 2024
STATUS
approved