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A093669
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Numbers having a unique representation as ab+ac+bc, with 0 < a < b < c.
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8
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11, 14, 17, 19, 20, 27, 32, 34, 36, 43, 46, 49, 52, 64, 67, 73, 82, 97, 100, 142, 148, 163, 193
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Are there more terms?
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REFERENCES
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LINKS
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EXAMPLE
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11 is on the list because 11 = 1*2+1*3+2*3.
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MATHEMATICA
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oneSol={}; Do[lim=Ceiling[(n-2)/3]; cnt=0; Do[If[n>a*b && Mod[n-a*b, a+b]==0 && Quotient[n-a*b, a+b]>b, cnt++; If[cnt>1, Break[]]], {a, 1, lim-1}, {b, a+1, lim}]; If[cnt==1, AppendTo[oneSol, n]], {n, 10000}]; oneSol
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PROG
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(Python)
from collections import Counter
def aupto(N):
acount = Counter()
for i in range(1, N-1):
for j in range(i+1, N//i + 1):
p, s = i*j, i+j
for k in range(j+1, (N-p)//s + 1):
acount.update([p + s*k])
return sorted([k for k in acount if acount[k] == 1])
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CROSSREFS
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Cf. A000926 (numbers not of the form ab+ac+bc, 0<a<b<c).
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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