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%I #12 Aug 04 2018 04:11:04
%S 0,0,0,0,1,0,1,0,1,0,2,0,1,1,1,0,2,0,2,1,1,0,3,0,1,1,2,0,3,0,2,1,1,1,
%T 3,0,1,1,3,0,3,0,2,2,1,0,4,0,2,1,2,0,3,1,3,1,1,0,5,0,1,2,2,1,3,0,2,1,
%U 3,0,5,0,1,2,2,1,3,0,4,1,1,0,5,1,1,1,3,0,5,1,2,1,1,1,5,0,2,2,3
%N Number of integer pairs (x,y) such that 0<x<y<=n and x*y=n+1.
%C For a guide to related sequences, see A211266.
%H Antti Karttunen, <a href="/A211159/b211159.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (A000005(1+n) - A010052(1+n) - 2)/2 = A200213(1+n)/2. - _Antti Karttunen_, Jul 07 2017
%e a(11) counts these pairs: (2,6), (3,4).
%t a = 1; b = n; z1 = 120;
%t t[n_] := t[n] = Flatten[Table[x*y, {x, a, b - 1}, {y, x + 1, b}]]
%t c[n_, k_] := c[n, k] = Count[t[n], k]
%t Table[c[n, n], {n, 1, z1}] (* A056924 *)
%t Table[c[n, n + 1], {n, 1, z1}] (* A211159 *)
%t Table[c[n, 2*n], {n, 1, z1}] (* A211261 *)
%t Table[c[n, 3*n], {n, 1, z1}] (* A211262 *)
%t Table[c[n, Floor[n/2]], {n, 1, z1}] (* A211263 *)
%t Print
%t c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
%t Table[c1[n, n], {n, 1, z1}] (* A211264 *)
%t Table[c1[n, n + 1], {n, 1, z1}] (* A211265 *)
%t Table[c1[n, 2*n], {n, 1, z1}] (* A211266 *)
%t Table[c1[n, 3*n], {n, 1, z1}] (* A211267 *)
%t Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A181972 *)
%o (PARI) A211159(n) = (numdiv(1+n)-issquare(1+n)-2)/2; \\ _Antti Karttunen_, Jul 07 2017
%o (Scheme) (define (A211159 n) (/ (- (A000005 (+ 1 n)) (A010052 (+ 1 n)) 2) 2)) ;; _Antti Karttunen_, Jul 07 2017
%Y Cf. A000005, A010052, A200213, A211266.
%K nonn
%O 1,11
%A _Clark Kimberling_, Apr 06 2012
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