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A349200
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Loeschian numbers of the form (x + y)*(x^2 + y^2).
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2
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0, 1, 4, 27, 64, 108, 156, 175, 256, 259, 343, 400, 729, 1261, 1372, 1417, 1728, 1875, 2197, 2916, 3439, 3492, 3667, 4096, 4212, 4579, 4725, 6175, 6859, 6912, 6993, 7104, 7825, 8112, 8125, 8425, 8788, 9261, 9264, 9325, 9925, 9984, 10800, 11200, 11425, 11712
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OFFSET
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1,3
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COMMENTS
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k is in this sequence if there exist numbers x, y, v, w such that k = x^2 + x*y + y^2 = (v + w)*(v^2 + w^2). We call (x, y, v, w) a witness of k. k can have different witnesses.
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LINKS
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FORMULA
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EXAMPLE
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729 = 27^2 + 27*0 + 0^2 = (9 + 0)*(9^2 + 0^2).
3492 = 48^2 + 48*18 + 18^2 = (13 + 5)*(13^2 + 5^2).
3667 = 53^2 + 53*13 + 13^2 = (12 + 7)*(12^2 + 7^2).
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PROG
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(Julia) # Returns the terms less than or equal to b^3.
# Uses the function isA003136 from A003136.
function A349200List(b)
b3 = b^3; R = [0]
for n in 1:b
for k in 0:n
a = (n + k) * (n^2 + k^2)
a > b3 && break
isA003136(a) && push!(R, a)
end end
sort(R) end
A349200List(24) |> println
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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