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A063649
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Largest b such that 1/n=1/c+1/b has integer solutions with c>b.
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4
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3, 4, 6, 6, 10, 8, 12, 12, 15, 12, 21, 14, 21, 24, 24, 18, 30, 20, 36, 30, 33, 24, 42, 30, 39, 36, 44, 30, 55, 32, 48, 44, 51, 60, 63, 38, 57, 52, 72, 42, 78, 44, 66, 72, 69, 48, 84, 56, 75, 68, 78, 54, 90, 80, 105, 76, 87, 60, 110, 62, 93, 112, 96, 90, 110, 68, 102, 92, 120
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OFFSET
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2,1
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COMMENTS
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Smallest b is (n+1) since 1/n = 1/(n(n+1))+1/(n+1).
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LINKS
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FORMULA
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a(n) = n + 1 if and only if n is prime. (End)
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EXAMPLE
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a(10)=15 since 1/10=1/20+1/20=1/30+1/15=1/35+1/14=1/60+1/12=1/110+1/11, but the first sum does not have c>b, leaving the second sum to provide the value.
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MAPLE
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f:= proc(n) local b;
for b from 2*n-1 by -1 do
if n*b mod (b-n) = 0 then return b fi
od
end proc:
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MATHEMATICA
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a[n_] := n + SelectFirst[Divisors[n^2] // Reverse, #<n&];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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