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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 10 2024
STATUS
approved