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A060775 Lower central (median) divisor of n. 8
1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 1, 3, 1, 4, 3, 2, 1, 4, 1, 2, 3, 4, 1, 5, 1, 4, 3, 2, 5, 4, 1, 2, 3, 5, 1, 6, 1, 4, 5, 2, 1, 6, 1, 5, 3, 4, 1, 6, 5, 7, 3, 2, 1, 6, 1, 2, 7, 4, 5, 6, 1, 4, 3, 7, 1, 8, 1, 2, 5, 4, 7, 6, 1, 8, 3, 2, 1, 7, 5, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,5

COMMENTS

Also: Largest divisor of n which is less than sqrt(n).

If n is not a square, then a(n) = A033676(n), else a(n) is strictly smaller than A033676(n) = sqrt(n).  - M. F. Hasler, Sep 20 2011

Record values occur for n = k * (k+1), for which a(n) = k. - Franklin T. Adams-Watters, May 01 2015

LINKS

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

FORMULA

a(n) = max { d|n ; d<n }  (where "|" means "divides").

EXAMPLE

n=252, D={1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252}, 18 divisors, the 9th is 14, so a(252)=14.

MATHEMATICA

Table[Part[Divisors[w], Floor[DivisorSigma[0, w]/2]], {w, 1, 256}]

PROG

(PARI) for (n=2, 1000, d=divisors(n); write("b060775.txt", n, " ", d[length(d)\2])) \\ Harry J. Smith, Jul 11 2009

(PARI) A060775(n)=divisors(n)[numdiv(n)\2] /* using "max(numdiv(n)\2, 1)" would yield a(1)=1; M. F. Hasler, Sep 21 2011 */

CROSSREFS

Cf. A033677, A000196, A000005, A000142, A027423, A055226, A060776, A060777, A002378.

Sequence in context: A045778 A033103 A245661 * A175494 A055399 A029426

Adjacent sequences:  A060772 A060773 A060774 * A060776 A060777 A060778

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 26 2001

STATUS

approved

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Last modified November 22 09:32 EST 2017. Contains 295076 sequences.