A063718 a(n) is the smallest divisor of n^2 that is greater than n.

4, 9, 8, 25, 9, 49, 16, 27, 20, 121, 16, 169, 28, 25, 32, 289, 27, 361, 25, 49, 44, 529, 32, 125, 52, 81, 49, 841, 36, 961, 64, 99, 68, 49, 48, 1369, 76, 117, 50, 1681, 49, 1849, 88, 75, 92, 2209, 64, 343, 100, 153, 104, 2809, 81, 121, 64, 171, 116, 3481, 72, 3721, 124

Offset: 2

Author

Vladeta Jovovic, Aug 12 2001

Keywords

• nonn

Comments

Larger of two distinct numbers with minimum sum whose geometric mean is n. E.g., a(12) = 16 as 12^2 = 144 = 1*144 = 2*72 = 3*48 = 4*36 = 6*24 = 8*18 = 9*16, etc. - Amarnath Murthy, Feb 15 2003

Examples

			a(45)=75 because divisors of 45^2 are {1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025} and the smallest element greater than 45 is 75.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 2..1000

Crossrefs

A063648(n) = n + a(n), A063717(n) = n^2/A063718(n), A063427(n) = n - a(n).

Cf. A063717.

Programs

Maple

with(numtheory): for n from 2 to 200 do a := divisors(n^2): b := a[(tau(n^2)-1)/2]: printf(`%d,`,n^2/b); od:

Mathematica

sdgn[n_]:=Select[Divisors[n^2],#>n&,1]; Flatten[Array[sdgn,70]] (* Harvey P. Dale, Jun 18 2012 *)

PARI

{ for (n=2, 1000, d=divisors(n^2); write("b063718.txt", n, " ", d[2 + length(d)\2]) ) } \\ Harry J. Smith, Aug 28 2009