A138224 a(n) is the divisor of n that is nearest to tau(n), the number of divisors of n. In case of a tie, take the smaller of those two divisors.

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

Offset

1,2

Links

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

Example

There are four divisors of 15: (1,3,5,15). There are two divisors, 3 and 5, that are nearest 4. Since there is a tie (4 is equidistant from 3 and 5), we take the smaller divisor, 3, so a(15) = 3.

Maple

A138224 := proc(n) if n = 1 then RETURN(1); fi; t := numtheory[tau](n) ; dvs := sort(convert(numtheory[divisors](n), list)) ; a := op(1, dvs) ; for i from 2 to nops(dvs) do if abs(op(i, dvs) - t) < abs(a-t) then a := op(i, dvs) ; fi; od: a ; end: seq(A138224(n), n=1..120) ; # R. J. Mathar, Jul 20 2009

Mathematica

nd[n_]:=Module[{div=Divisors[n]}, Nearest[div, Length[div]][[1]]]; Array[ nd, 110] (* Harvey P. Dale, Jun 17 2018 *)

Prog

(PARI) A138224(n) = { my(pd=0, u=numdiv(n)); fordiv(n, d, if(d>u, return(if((d-u)<(u-pd), d, pd))); pd=d); (pd); }; \\ Antti Karttunen, Apr 01 2021

Crossrefs

Cf. A000005, A138221, A138222, A138223.

Sequence in context: A029216 A153174 A138222 * A181472 A271825 A271875

Adjacent sequences: A138221 A138222 A138223 * A138225 A138226 A138227

Keyword

nonn

Author

Leroy Quet, Mar 06 2008

Extensions

Extended beyond a(15) by R. J. Mathar, Jul 20 2009

Status

approved