%I A025478
%S A025478 1,2,2,3,2,5,3,2,6,7,2,3,10,11,5,2,12,13,14,6,15,3,2,17,18,7,19,20,21,
               22,
%T A025478 2,23,24,5,26,3,28,29,30,31,10,2,33,34,35,6,11,37,38,39,40,41,12,42,43,
%U A025478 44,45,2,46,3,13,47,48,7,50,51,52,14,53,54,55,5,56,57,58,15,59,60,61,62
%N A025478 Least roots of perfect powers (A001597).
%H A025478 Daniel Forgues, <a href="b025478.txt">Table of n, a(n) for n=1..10000</
               a>
%F A025478 (i) a(n) < n for n>2. (ii) a(n)/n is bounded and lim sup a(n)/n must 
               be around 0.7. (iii) sum(k=1, k, a(k)) seems to be asymptotic to 
               c*n^2 with c around 0.29. (iv) a(n) = 2 if n is in A070228 (proof 
               seems self-evident), hence there's no asymptotic expression for a(n) 
               (just the average in (iii)). - Benoit Cloitre, Oct 14, 2002
%e A025478 a(5)=2 because pp(5)=16=2^4 (not 4^2 as we take the smallest base).
%t A025478 pp = Select[ Range[5000], Apply[GCD, Last[ Transpose[ FactorInteger[ 
               # ]]]] > 1 &]; f[n_] := Block[{b = 2}, While[ !IntegerQ[ Log[b, pp[[n]]]], 
               b++ ]; b]; Join[{1}, Table[ f[n], {n, 2, 80}]]
%Y A025478 a(n) = A052410(A001597(n)).
%Y A025478 Cf. A025479 Largest exponents of perfect powers (A001597).
%Y A025478 Cf. A001597 Perfect powers: m^k where m is an integer and k >= 2.
%Y A025478 Sequence in context: A076397 A076403 A157987 this_sequence A084371 A025476 
               A078773
%Y A025478 Adjacent sequences: A025475 A025476 A025477 this_sequence A025479 A025480 
               A025481
%K A025478 easy,nonn
%O A025478 1,2
%A A025478 David W. Wilson (davidwwilson(AT)comcast.net)
%E A025478 Added cross-reference. Definition edited by Daniel Forgues (squid(AT)zensearch.com), 
               Mar 10 2009