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A162348 List of pairs (i,j) of central factors of n, such that i*j = n, where i is the largest divisor of n <= sqrt(n) and j is the smallest divisor of n >= sqrt(n).

%I A162348 #16 Aug 26 2022 19:49:01
%S A162348 1,1,1,2,1,3,2,2,1,5,2,3,1,7,2,4,3,3,2,5,1,11,3,4,1,13,2,7,3,5,4,4,1,
%T A162348 17,3,6,1,19,4,5,3,7,2,11,1,23,4,6,5,5,2,13,3,9,4,7,1,29,5,6,1,31,4,8,
%U A162348 3,11,2,17,5,7,6,6,1,37,2,19,3,13,5,8,1,41,6,7,1,43,4,11,5,9,2,23,1,47,6,8,7
%N A162348 List of pairs (i,j) of central factors of n, such that i*j = n, where i is the largest divisor of n <= sqrt(n) and j is the smallest divisor of n >= sqrt(n).
%C A162348 Note that if n is a square then the square root of n appears repeated: i = j = sqrt(n).
%C A162348 Squarest (least oblong) integral rectangle with area n. This has minimal semiperimeter (A063655), since s = i + j = i + n/i is minimal when ds/di = 1 - n/i^2 = 0, i.e., n = i^2. - _Daniel Forgues_, Sep 29 2014
%H A162348 Alois P. Heinz, <a href="/A162348/b162348.txt">Table of n, a(n) for n = 1..20000</a>
%t A162348 f[n_] := Block[{d = Divisors@n}, len = Length[d]/2; {d[[Ceiling@len]], d[[Floor[len + 1]] ]}]; f[1] = {1, 1}; Array[f, 49] // Flatten (* _Robert G. Wilson v_, Aug 17 2009 *)
%Y A162348 Cf. A033676, A033677, A018253, A160812, A161344, A006446, A162190.
%K A162348 easy,nonn
%O A162348 1,4
%A A162348 _Omar E. Pol_, Jul 04 2009
%E A162348 a(35) and further terms from _Robert G. Wilson v_, Aug 17 2009; corrected Aug 18 2009