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

2,1

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Cf. A063717.

Sequence in context: A140580 A289280 A077662 * A063748 A121920 A318279

Adjacent sequences: A063715 A063716 A063717 * A063719 A063720 A063721

Keyword

nonn

Author

Vladeta Jovovic, Aug 12 2001

Status

approved