A063717 a(n) is the greatest divisor of n^2 that is less than n.

1, 1, 2, 1, 4, 1, 4, 3, 5, 1, 9, 1, 7, 9, 8, 1, 12, 1, 16, 9, 11, 1, 18, 5, 13, 9, 16, 1, 25, 1, 16, 11, 17, 25, 27, 1, 19, 13, 32, 1, 36, 1, 22, 27, 23, 1, 36, 7, 25, 17, 26, 1, 36, 25, 49, 19, 29, 1, 50, 1, 31, 49, 32, 25, 44, 1, 34, 23, 50, 1, 64, 1, 37, 45, 38, 49, 52, 1, 64, 27, 41

Offset: 2

Author

Vladeta Jovovic, Aug 12 2001

Keywords

• nonn

Comments

Smaller of two distinct numbers with minimum sum whose geometric mean is n. E.g., a(12) = 9 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)=27 because set of divisors of 45^2 is {1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025} and the greatest element of the set less than 45 is 27.
		

Links

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

Crossrefs

A063649(n) = n + a(n), A063718(n) = n^2/A063717(n), A063428(n) = n - a(n).

Cf. A063718.

Programs

Maple

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

Mathematica

f[n_] := Module[{dn2 = Divisors[n^2]}, Last[Take[dn2, {1, Flatten[Position[dn2, n]][[ 1]] - 1}]]]; Table[f[i], {i, 2, 85}]
Table[Select[Divisors[n^2],#Harvey P. Dale, Apr 23 2016 *)

PARI

{ for (n=2, 1000, d=divisors(n^2); write("b063717.txt", n, " ", d[length(d)\2]) ) } \\ Harry J. Smith, Aug 28 2009