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A081676
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Largest perfect power <= n.
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2
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1, 1, 1, 4, 4, 4, 4, 8, 9, 9, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 16, 16, 16, 25, 25, 27, 27, 27, 27, 27, 32, 32, 32, 32, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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MAPLE
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N:= 1000: # to get a(1) to a(N).
Powers:= {1, seq(seq(b^p, p=2..floor(log[b](N))), b=2..isqrt(N))}:
Powers:= sort(convert(Powers, list)):
j:= 1:
for i from 1 to N do
if i >= Powers[j+1] then j:= j+1 fi;
A[i]:= Powers[j];
od:
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MATHEMATICA
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Array[SelectFirst[Range[#, 1, -1], Or[And[! PrimeQ@ #, GCD @@ FactorInteger[#][[All, -1]] > 1], # == 1] &] &, 72] (* Michael De Vlieger, Jun 14 2017 *)
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PROG
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(PARI) a(n) = {while(!ispower(n), n--; if (n==0, return (1))); n; } \\ Michel Marcus, Nov 04 2015
(Sage)
p = [i for i in (1..81) if i.is_perfect_power()]
r = [[p[i]]*(p[i+1]-p[i]) for i in (0..10)]
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CROSSREFS
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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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