A126081 a(n) = number of k, 1 <= k <= n, such that k divides ceiling(n/k).

1, 1, 2, 2, 1, 1, 3, 3, 2, 1, 2, 2, 2, 2, 3, 4, 2, 2, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 2, 2, 4, 4, 2, 3, 4, 4, 1, 1, 2, 2, 1, 1, 4, 4, 4, 4, 5, 5, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 5, 4, 1, 1, 3, 3, 2, 3, 5, 5, 3, 3, 4, 3, 3, 3, 5, 5, 3, 1, 2, 2, 1, 1, 2, 3, 2, 2, 3, 4, 4, 4, 5, 6, 5, 5, 5, 4, 1, 1, 3, 3, 2

Offset

1,3

Links

Table of n, a(n) for n=1..105.

Example

Ceiling(n/k) for n = 7 is: k=1: 7; k=2: 4; k=3: 3; k=4: 2; k=5: 2; k=6: 2; k=7: 1. 1 divides 7, 2 divides 4, 3 divides 3; so a(7) = 3.

Maple

a:=proc(n) local ct, k: ct:=0: for k from 1 to n do if type(ceil(n/k)/k, integer)=true then ct:=ct+1 else ct:=ct fi od: ct; end: seq(a(n), n=1..130); # Emeric Deutsch, Mar 28 2007

Mathematica

Table[c=0; Do[If[Divisible[Ceiling[n/k], k], c++], {k, n}]; c, {n, 105}] (* James C. McMahon, Dec 24 2024 *)

Crossrefs

Cf. A066030.

Sequence in context: A155092 A095133 A334572 * A268507 A272351 A243612

Adjacent sequences: A126078 A126079 A126080 * A126082 A126083 A126084

Keyword

nonn,changed

Author

Leroy Quet, Mar 02 2007

Extensions

More terms from Emeric Deutsch, Mar 28 2007

Status

approved