|
%I #11 Jun 16 2020 08:33:51
%S 0,1,1,2,2,3,1,3,2,4,1,4,1,2,1,3,3,4,1,4,1,2,1,3,1,3,1,3,1,4,1,4,2,3,
%T 1,4,2,2,1,3,1,3,1,2,1,2,1,3,1,4,1,2,1,3,1,3,1,2,1,2,1,2,1,3,4,3,1,4,
%U 1,2,1,5,1,2,1,2,1,2,1,4,1,4,1,3,1,2,1,2,1,4,1,2,1,2,1,3,1,3,1,2
%N Number of ways to write n = x^i + x^j with 1<x<=n and 0<=i<=j.
%C a(A088905(n)) = 1;
%C a(A088906(n)) = n and a(k) < n for 1 <= k < A088906(n).
%H Robert Israel, <a href="/A088904/b088904.txt">Table of n, a(n) for n = 1..10000</a>
%e a(32)=4: 32 = 2^4+2^4 = 4^2+4^2 = 16^1+16^1 = 31^0+31^1;
%e a(33)=2: 33 = 2^0+2^5 = 32^0+32^1;
%e a(34)=3: 34 = 2^1+2^5 = 17^1+17^1 = 33^0+33^1.
%p N:= 200:
%p V:= Vector(N,i -> 2-(i mod 2)):
%p for x from 2 while 1 + x^2 <= N do
%p for i from 0 while 2*x^i <= N do
%p for j from max(2,i) do
%p t:= x^i + x^j;
%p if t > N then break fi;
%p V[t]:= V[t]+1
%p od od od:
%p V[1]:= 0: V[2]:= 1:
%p convert(V,list); # _Robert Israel_, Mar 27 2020
%t M = 200;
%t V = 2 - Mod[Range[M], 2];
%t For[x = 2, 1 + x^2 <= M, x++, For[i = 0, 2 x^i <= M, i++, For[j = Max[2, i], True, j++, t = x^i + x^j; If[t > M, Break[]]; V[[t]]++]]];
%t V[[1]] = 0; V[[2]] = 1;
%t V (* _Jean-François Alcover_, Jun 15 2020, after _Robert Israel_ *)
%K nonn
%O 1,4
%A Entry completely revised: _Hugo Pfoertner_ and _Reinhard Zumkeller_, Oct 20 2004
|
