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A375739
Maximum of the n-th maximal anti-run of adjacent (increasing by more than one at a time) non-perfect-powers.
6
2, 5, 6, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 23, 28, 29, 30, 33, 34, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88
OFFSET
1,1
COMMENTS
Non-perfect-powers (A007916) are numbers with no proper integer roots.
An anti-run of a sequence is an interval of positions at which consecutive terms differ by more than one.
Also non-perfect-powers x such that x + 1 is also a non-perfect-power.
EXAMPLE
The initial anti-runs are the following, whose maxima are a(n):
(2)
(3,5)
(6)
(7,10)
(11)
(12)
(13)
(14)
(15,17)
(18)
(19)
(20)
(21)
(22)
(23)
(24,26,28)
MATHEMATICA
radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
Max/@Split[Select[Range[100], radQ], #1+1!=#2&]//Most
- or -
radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
Select[Range[100], radQ[#]&&radQ[#+1]&]
CROSSREFS
For nonprime numbers we have A068780, runs A006093 with 2 removed.
For squarefree numbers we have A007674, runs A373415.
For nonsquarefree numbers we have A068781, runs A072284 minus 1 and shifted.
For prime-powers we have A006549, runs A373674.
For non-prime-powers we have A255346, runs A373677.
For anti-runs of non-perfect-powers:
- length: A375736
- first: A375738
- last: A375739 (this)
- sum: A375737
For runs of non-perfect-powers:
- length: A375702
- first: A375703
- last: A375704
- sum: A375705
A001597 lists perfect-powers, differences A053289.
A007916 lists non-perfect-powers, differences A375706.
Sequence in context: A337298 A184418 A112967 * A244731 A307562 A109150
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 10 2024
STATUS
approved