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%I #31 Mar 08 2020 11:08:06
%S 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,
%T 27,27,27,32,32,32,32,36,36,36,36,36,36,36,36,36,36,36,36,36,49,49,49,
%U 49,49,49,49,49,49,49,49,49,49,49,49,64,64,64,64,64,64,64,64,64,64,64
%N Largest perfect power <= n.
%C a(n) = n if n is in A001597, otherwise a(n) = a(n-1). - _Robert Israel_, Dec 17 2015
%H Neven Sajko, <a href="/A081676/b081676.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n - A069584(n).
%p N:= 1000: # to get a(1) to a(N).
%p Powers:= {1,seq(seq(b^p, p=2..floor(log[b](N))),b=2..isqrt(N))}:
%p Powers:= sort(convert(Powers,list)):
%p j:= 1:
%p for i from 1 to N do
%p if i >= Powers[j+1] then j:= j+1 fi;
%p A[i]:= Powers[j];
%p od:
%p seq(A[i],i=1..N); # _Robert Israel_, Dec 17 2015
%t Array[SelectFirst[Range[#, 1, -1], Or[And[! PrimeQ@ #, GCD @@ FactorInteger[#][[All, -1]] > 1], # == 1] &] &, 72] (* _Michael De Vlieger_, Jun 14 2017 *)
%o (PARI) a(n) = {while(!ispower(n), n--; if (n==0, return (1))); n;} \\ _Michel Marcus_, Nov 04 2015
%o (Sage)
%o p = [i for i in (1..81) if i.is_perfect_power()]
%o r = [[p[i]]*(p[i+1]-p[i]) for i in (0..10)]
%o print([y for x in r for y in x]) # _Peter Luschny_, Jun 13 2017
%Y Cf. A001597, A069584.
%K nonn
%O 1,4
%A _Reinhard Zumkeller_, Mar 26 2003
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