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%I #45 Jan 18 2021 09:52:46
%S 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,
%T 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,
%U 0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,2,0,0,0
%N Number of ordered pairs (i,j) such that i*j=n and i+j is a square.
%C a(n)=1 for n>0 in A141046.
%C 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
%H Reinhard Zumkeller, <a href="/A211996/b211996.txt">Table of n, a(n) for n = 1..10000</a>
%H D. Clark, <a href="http://dx.doi.org/10.4153/CMB-1991-029-4">An arithmetical function associated with the rank of elliptic curves</a>, Canad. Math. Bull. Vol. 34 (2), 1991 pp. 181-185.
%e 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.
%t nop[n_]:=Module[{divs=Divisors[n]},Count[Thread[{divs,Reverse[divs]}], _?(IntegerQ[Sqrt[Total[#]]]&)]]; Array[nop,90] (* _Harvey P. Dale_, Nov 08 2012 *)
%o (Haskell)
%o a211996 n = length [x | x <- [1..n], let (y, m) = divMod n x,
%o m == 0, a010052 (x + y) == 1]
%o -- _Reinhard Zumkeller_, Oct 28 2012
%o (PARI) a(n) = sumdiv(n, d, issquare(d+n/d)); \\ _Michel Marcus_, Jan 18 2021
%Y Cf. A010052.
%K nonn
%O 1,3
%A _Michel Marcus_, Oct 25 2012
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