%I A103840
%S A103840 1,0,0,0,1,0,0,0,1,1,0,0,1,0,0,0,2,1,0,0,1,0,0,0,2,2,0,1,1,0,0,1,2,2,0,
%T A103840 0,3,0,0,0,2,2,0,2,2,0,0,1,2,3,0,0,4,0,0,0,2,3,0,2,2,0,0,2,4,3,0,0,5,0,
%U A103840 0,0,3,4,0,2,3,0,0,2,5,5,0,0,5,1,0,0,3,7,1,3,3,1,0,2,5,5,1,0,7,0,0,0,3
%N A103840 Number of ways to represent n as a sum of b^e with b >= 2, e >= 2, e 
               distinct.
%C A103840 291 is the largest number that cannot be expressed in this way.
%F A103840 G.f.: Prod(e >= 2, 1 + Sum(b >= 2, x^(b^e))).
%e A103840 68 = 2^2+4^3 = 2^2+2^6 = 3^2+3^3+2^5 = 5^2+3^3+2^4 = 6^2+2^5 so a(68) 
               = 5. Note that although 4^3 = 2^6, the exponents are different and 
               so 2^2+4^3 and 2^2+2^6 are counted as distinct.
%Y A103840 Cf. A103841 (where a(n) = 0), A103843 (positions of records).
%Y A103840 Sequence in context: A025435 A160382 A081221 this_sequence A066301 A046660 
               A108730
%Y A103840 Adjacent sequences: A103837 A103838 A103839 this_sequence A103841 A103842 
               A103843
%K A103840 nonn
%O A103840 1,17
%A A103840 Gordon Hamilton (hamiltonian(AT)shaw.ca), Mar 29 2005
%E A103840 More terms from David W. Wilson (davidwwilson(AT)comcast.net), Mar 30 
               2005
%E A103840 More terms from David Wasserman (dwasserm(AT)earthlink.net), Apr 24 2008