

A343397


Number of ways to write n as 2^x + [y^2/3] + [z^2/4] with x,y,z positive integers, where [.] is the floor function.


10



0, 1, 2, 3, 4, 4, 5, 5, 8, 5, 9, 5, 8, 8, 6, 9, 9, 10, 8, 11, 10, 10, 9, 9, 14, 8, 8, 10, 12, 11, 6, 14, 13, 10, 12, 13, 15, 11, 13, 9, 20, 6, 12, 17, 13, 13, 10, 11, 17, 12, 11, 13, 15, 14, 9, 13, 13, 14, 11, 18, 11, 15, 7, 12, 22, 13, 14, 17, 17, 11, 15, 13, 24, 16, 9, 17, 15, 15, 14, 18
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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.


LINKS



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[nFloor[x^2/3]Floor[y^2/4]], r=r+1], {x, 1, Sqrt[3n1]}, {y, 1, Sqrt[4(nFloor[x^2/3]1)+1]}]; tab=Append[tab, r], {n, 1, 80}]; Print[tab]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



