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A088905
Numbers m having exactly one representation m = x^i + x^j with 1<x<=m and 0<=i<=j.
3
2, 3, 7, 11, 13, 15, 19, 21, 23, 25, 27, 29, 31, 35, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 131, 133, 135, 137, 139, 141
OFFSET
1,1
COMMENTS
A088904(a(n)) = 1.
All terms > 2 are odd. - Robert Israel, Dec 05 2019
LINKS
MAPLE
filter:= proc(n) local F, t, d, s, r, b;
F:= ifactors(n-1)[2];
d:= igcd(seq(t[2], t=F));
if d > 1 then return false fi;
for s in numtheory:-divisors(n) minus {1, n} do
r:= n/s-1;
F:= ifactors(s)[2];
d:= igcd(seq(t[2], t=F));
b:= mul(t[1]^(t[2]/d), t=F);
if r = b^padic:-ordp(r, b) then return false fi
od;
true
end proc:
select(filter, [2, seq(i, i=3..1000, 2)]); # Robert Israel, Dec 05 2019
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;
Position[V, 1] // Flatten (* Jean-François Alcover, Jun 17 2020, after Robert Israel in A088904 *)
CROSSREFS
Sequence in context: A176363 A067991 A114600 * A045319 A178943 A038613
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 21 2003
EXTENSIONS
Entry completely revised: Hugo Pfoertner and Reinhard Zumkeller, Oct 20 2004
STATUS
approved