A138222 a(n) = the largest divisor of n that is <= the number of positive divisors of n.

1, 2, 1, 2, 1, 3, 1, 4, 3, 2, 1, 6, 1, 2, 3, 4, 1, 6, 1, 5, 3, 2, 1, 8, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 9, 1, 2, 3, 8, 1, 7, 1, 4, 5, 2, 1, 8, 1, 5, 3, 4, 1, 6, 1, 8, 3, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 4, 3, 7, 1, 12, 1, 2, 5, 4, 1, 6, 1, 10, 3, 2, 1, 12, 1, 2, 3, 8, 1, 10, 1, 4, 3, 2, 1, 12, 1, 2, 3, 5, 1, 6, 1

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Example

There are four positive divisors of 15: (1,3,5,15). The largest of these divisors that is <=4 is 3; so a(15) = 3.

Maple

A138222 := proc(n) t := numtheory[tau](n) ; dvs := sort(convert(numtheory[divisors](n), list)) ; for i from 1 do if op(-i, dvs) <= t then RETURN( op(-i, dvs)) ; fi; od: end: seq(A138222(n), n=1..100) ; # R. J. Mathar, Jul 20 2009

Mathematica

Table[Last[Select[Divisors[n], #<=DivisorSigma[0, n]&]], {n, 120}]  (* Harvey P. Dale, Apr 04 2011 *)

Prog

(PARI) A138222(n) = { my(pd=0, u=numdiv(n)); fordiv(n, d, if(d>u, return(pd)); pd=d); (pd); }; \\ Antti Karttunen, Apr 01 2021

Crossrefs

Cf. A000005, A138221, A138223, A138224.

Sequence in context: A029229 A029216 A153174 * A138224 A181472 A271825

Adjacent sequences: A138219 A138220 A138221 * A138223 A138224 A138225

Keyword

nonn

Author

Leroy Quet, Mar 06 2008

Extensions

Extended beyond a(16) by R. J. Mathar, Jul 20 2009

Status

approved