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).

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, 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, 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

Offset: 1

Author

Omar E. Pol, Jul 04 2009

Keywords

• easy
• nonn

Comments

Note that if n is a square then the square root of n appears repeated: i = j = sqrt(n).

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A033676, A033677, A018253, A160812, A161344, A006446, A162190.

Programs

Mathematica

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 *)

Extensions

a(35) and further terms from Robert G. Wilson v, Aug 17 2009; corrected Aug 18 2009