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A088904 Number of ways to write n = x^i + x^j with 1<x<=n and 0<=i<=j. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 30 12:16 EST 2023. Contains 359943 sequences. (Running on oeis4.)