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A060292
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At least two unordered triples of positive numbers have product n and equal sums.
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3
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36, 40, 72, 90, 96, 126, 144, 168, 176, 200, 225, 234, 240, 252, 270, 280, 288, 297, 320, 360, 396, 408, 420, 432, 450, 480, 504, 520, 540, 546, 550, 560, 576, 588, 600, 630, 648, 672, 675, 690, 714, 720, 735, 736, 768, 780, 784, 800, 816, 840, 850, 855
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OFFSET
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1,1
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LINKS
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EXAMPLE
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36=6*6*1=9*2*2. 6+6+1=9+2+2. so 36 is in the sequence.
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MAPLE
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N:= 1000: # to get all entries <= N
for i from 1 to N do R[i]:= {} od:
A:= {}:
for a from 1 to floor(N^(1/3)) do
for b from a to floor((N/a)^(1/2)) do
for c from b to floor(N/(a*b)) do
p:= a*b*c;
s:= a+b+c;
if member(s, R[p]) then A:= A union {p}
else R[p]:= R[p] union {s}
fi;
od od od:
A;
# if using Maple 11 or earlier, uncomment the next line
# second Maple program:
b:= proc(n, k, t) option remember; expand(`if`(t=0, `if`(k<n, 0, x^n),
add(`if`(d>k, 0, b(n/d, d, t-1)*x^d), d=numtheory[divisors](n))))
end:
a:= proc(n) option remember; local k; for k from 1+
`if`(n=1, 0, a(n-1)) while max(coeffs(b(k$2, 2)))<2 do od; k
end:
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MATHEMATICA
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b[n_, k_, t_] := b[n, k, t] = Expand[If[t == 0, If[k < n, 0, x^n], Sum[If[d > k, 0, b[n/d, d, t - 1] x^d], {d, Divisors[n]}]]];
a[n_] := a[n] = Module[{k}, For[k = 1 + If[n == 1, 0, a[n - 1]], Max[ CoefficientList[b[k, k, 2], x]] < 2, k++]; k];
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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