OFFSET
1,3
COMMENTS
Conjecture: a(n) > 0 for all n > 1.
We have verified a(n) > 0 for all n = 2..2*10^6.
Conjecture verified up to 10^10. - Giovanni Resta, Apr 14 2021
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Zhi-Wei Sun, Natural numbers represented by [x^2/a] + [y^2/b] + [z^2/c], arXiv:1504.01608 [math.NT], 2015.
EXAMPLE
a(2) = 1 with 2 = 2^1 + [1^2/3] + [1^2/4].
a(3) = 2 with 3 = 2^1 + [1^2/3] + [2^2/4] = 2^1 + [2^2/3] + [1^2/4].
MATHEMATICA
PowQ[n_]:=PowQ[n]=n>1&&IntegerQ[Log[2, n]];
tab={}; Do[r=0; Do[If[PowQ[n-Floor[x^2/3]-Floor[y^2/4]], r=r+1], {x, 1, Sqrt[3n-1]}, {y, 1, Sqrt[4(n-Floor[x^2/3]-1)+1]}]; tab=Append[tab, r], {n, 1, 80}]; Print[tab]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Apr 13 2021
STATUS
approved