%I A005934 M3333
%S A005934 1,4,8,16,32,64,128,144,216,288,432,864,1296,1728,2592,3456,5184,7776,
%T A005934 10368,15552,20736,31104,41472,62208,86400,108000,129600,194400,216000,
%U A005934 259200,324000,432000,518400,648000,972000,1296000,1944000,2592000
%N A005934 Highly powerful numbers.
%D A005934 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005934 G. E. Hardy and M. V. Subbarao, Highly powerful numbers, Congress. Numer. 
               37 (1983), 277-307.
%D A005934 C. B. Lacampagne and J. L. Selfridge, Large highly powerful numbers are 
               cubeful, Proc. Amer. Math. Soc., 91 (1984), 173-181.
%H A005934 T. D. Noe, <a href="b005934.txt">Table of n, a(n) for n=1..300</a>
%H A005934 <a href="Sindx_Pow.html#powerful">Index entries for sequences related 
               to powerful numbers</a>
%F A005934 For n = Prod p_i^e_i, let b(n) = Prod e_i; then n is highly powerful 
               if b(n) sets a new record.
%o A005934 (PARI) {prdex(n)=local(s,fac); s=1; fac=factor(n); for(k=1,matsize(fac)[1],
               s=s*fac[k,2]); return(s)} {hp(m)=local(rec); rec=0; for(n=1,m,if(prdex(n)>
               rec,rec=prdex(n); print1(n",")))}
%Y A005934 Cf. A036965, A001694, A007532, A005934, A005188, A003321, A014576, A023052, 
               A046074.
%Y A005934 Cf. A085629
%Y A005934 Sequence in context: A145108 A108569 A111073 this_sequence A085629 A046055 
               A020707
%Y A005934 Adjacent sequences: A005931 A005932 A005933 this_sequence A005935 A005936 
               A005937
%K A005934 nonn,nice,easy
%O A005934 1,2
%A A005934 N. J. A. Sloane (njas(AT)research.att.com).
%E A005934 Hardy and Subbarao give an extensive table.
%E A005934 Corrected and extended by Jason Earls (zevi_35711(AT)yahoo.com), Jul 
               10 2003