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A033831
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Number of numbers d dividing n such that d >= 3 and n/d <= d-2.
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11
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0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 3, 2, 2, 1, 6, 1, 2, 3, 3, 2, 4, 1, 3, 2, 4, 1, 5, 1, 2, 3, 3, 2, 4, 1, 5, 2, 2, 1, 6, 2, 2, 2, 4, 1, 5, 2, 3, 2, 2, 2, 6, 1, 3, 3, 4, 1, 4, 1, 4, 4
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OFFSET
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1,8
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LINKS
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FORMULA
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MAPLE
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with(numtheory): for n from 1 to 200 do it := divisors(n): count := 0: for i from 1 to nops(it) do if it[i]>=3 and 1<=n/it[i] and n/it[i]<=(it[i]-2) then count := count+1 fi :od: printf(`%d, `, count) od:
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MATHEMATICA
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a[n_] := DivisorSum[n, 1&, # > 2 && n/# < #-1 &]; Array[a, 100] (* Amiram Eldar, Jun 11 2019 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, (d>=3) && (q=n/d) && (q>=1) && (q<=d-2)); \\ Michel Marcus, Nov 05 2014
(PARI) a033831(n) = numdiv(n)\2 - issquare(4*n+1); \\ Max Alekseyev, Oct 09 2023
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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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