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A211996
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Number of ordered pairs (i,j) such that i*j=n and i+j is a square.
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3
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0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0
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OFFSET
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1,3
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COMMENTS
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a(8820)=8 and it is the only term in the first 10000 terms that is greater than 6. There are 977 terms in the first 10000 terms that are greater than zero. - Harvey P. Dale, Nov 08 2012
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LINKS
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EXAMPLE
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For n=3, the pairs (a,b) such that a*b=3 are (1,3) and (3,1). Both pairs add up to a square, so a(3) = 2.
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MATHEMATICA
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nop[n_]:=Module[{divs=Divisors[n]}, Count[Thread[{divs, Reverse[divs]}], _?(IntegerQ[Sqrt[Total[#]]]&)]]; Array[nop, 90] (* Harvey P. Dale, Nov 08 2012 *)
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PROG
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(Haskell)
a211996 n = length [x | x <- [1..n], let (y, m) = divMod n x,
m == 0, a010052 (x + y) == 1]
(PARI) a(n) = sumdiv(n, d, issquare(d+n/d)); \\ Michel Marcus, Jan 18 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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