A138223 a(n) = the nearest divisor of n to the number of positive divisors of n. In case of tie, round up.

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

Offset

1,2

Links

Table of n, a(n) for n=1..101.

Example

There are four positive divisors of 15: (1,3,5,15). There are two divisors, 3 and 5, that are nearest 4. We take the larger divisor, 5 in this case, in case of a tie; so a(15) = 5.

Maple

A138223 := 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(A138223(n), n=1..120) ; # R. J. Mathar, Jul 20 2009

Mathematica

a[n_] := With[{d = Divisors[n]}, Nearest[d, Length[d]][[-1]]];
Table[a[n], {n, 1, 101}] (* Jean-François Alcover, Oct 18 2023 *)

Crossrefs

Cf. A138221, A138222, A138224, A000005.

Sequence in context: A337210 A361258 A141063 * A194742 A159798 A294236

Adjacent sequences: A138220 A138221 A138222 * A138224 A138225 A138226

Keyword

nonn

Author

Leroy Quet, Mar 06 2008

Extensions

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

Status

approved