A088904 Number of ways to write n = x^i + x^j with 1<x<=n and 0<=i<=j.

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, 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, 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

Offset

1,4

Comments

a(A088905(n)) = 1;

a(A088906(n)) = n and a(k) < n for 1 <= k < A088906(n).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(32)=4: 32 = 2^4+2^4 = 4^2+4^2 = 16^1+16^1 = 31^0+31^1;
a(33)=2: 33 = 2^0+2^5 = 32^0+32^1;
a(34)=3: 34 = 2^1+2^5 = 17^1+17^1 = 33^0+33^1.

Maple

N:= 200:
V:= Vector(N, i -> 2-(i mod 2)):
for x from 2 while 1 + x^2 <= N do
  for i from 0 while 2*x^i <= N do
    for j from max(2, i) do
       t:= x^i + x^j;
       if t > N then break fi;
       V[t]:= V[t]+1
od od od:
V[1]:= 0: V[2]:= 1:
convert(V, list); # Robert Israel, Mar 27 2020

Mathematica

M = 200;
V = 2 - Mod[Range[M], 2];
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]]++]]];
V[[1]] = 0; V[[2]] = 1;
V (* Jean-François Alcover, Jun 15 2020, after Robert Israel *)

Crossrefs

Sequence in context: A304092 A339669 A171691 * A241568 A335017 A047972

Adjacent sequences: A088901 A088902 A088903 * A088905 A088906 A088907

Keyword

nonn

Author

Entry completely revised: Hugo Pfoertner and Reinhard Zumkeller, Oct 20 2004

Status

approved