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

2,3

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

Links

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

Example

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.

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], #<n&][[-1]], {n, 2, 100}] (* Harvey P. Dale, Apr 23 2016 *)

Prog

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

Crossrefs

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

Cf. A063718.

Sequence in context: A321437 A319711 A319713 * A024994 A243329 A051953

Adjacent sequences: A063714 A063715 A063716 * A063718 A063719 A063720

Keyword

nonn

Author

Vladeta Jovovic, Aug 12 2001

Status

approved