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A359225
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Numbers that can be expressed as (a^3 + b^3)/(a*b) with b > a >= 1.
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2
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9, 18, 27, 28, 35, 36, 45, 54, 56, 63, 65, 70, 72, 81, 84, 90, 91, 99, 105, 108, 112, 117, 126, 130, 133, 135, 140, 144, 152, 153, 162, 168, 171, 175, 180, 182, 189, 195, 196, 198, 207, 210, 216, 217, 224, 225, 234, 243, 245, 252, 260, 261, 266, 270, 273, 279, 280, 288, 297
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OFFSET
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1,1
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COMMENTS
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Numbers k such that k*a*b = a^3 + b^3 has integer solutions with b > a >= 1.
Numbers of the form r*(s^3 + t^3) with r >= 1 and s > t >= 1, by a = r*s*t^2, b = r*s^2*t.
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LINKS
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EXAMPLE
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63 can be expressed as (14^3 + 28^3)/(14*28) so 63 is a term.
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MATHEMATICA
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n = 300; Union@
Sort@Flatten@
Table[r*(s^3 + t^3), {r, 1, n/9}, {s, 1,
CubeRoot[n/(2*r) - 1]}, {t, s + 1, CubeRoot[n/r - s^3]}]
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PROG
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(Python)
def aupto(limit):
c=[k**3 for k in range(1, limit) if k**3<=limit]
s=set()
for i in range(len(c)):
for j in range(i+1, len(c)):
t=(c[i]+c[j])
for r in range(1, limit//t+1) :
s.add(r*t)
return(sorted(s))
print(aupto(500))
(MATLAB)
OneToN = [1:max_n]; a = [];
for n = 1:max_n-1
A = (OneToN(1:n)'*ones(1, max_n-n)).^3 ...
+ (ones(n, 1)*OneToN(n+1:end)).^3;
a = unique([a reshape(A(:), 1, numel(A))]);
a = a(1:min(length(a), max_n));
end
A = a'*OneToN;
a = unique(A(:)); a = a(1:min(length(a), max_n))';
end
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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