A243982 Number of divisors of n minus the number of parts in the symmetric representation of sigma(n).

0, 1, 0, 2, 0, 3, 0, 3, 0, 2, 0, 5, 0, 2, 1, 4, 0, 5, 0, 5, 0, 2, 0, 7, 0, 2, 0, 5, 0, 7, 0, 5, 0, 2, 1, 8, 0, 2, 0, 7, 0, 7, 0, 4, 3, 2, 0, 9, 0, 3, 0, 4, 0, 7, 0, 7, 0, 2, 0, 11, 0, 2, 1, 6, 0, 7, 0, 4, 0, 5, 0, 11, 0, 2, 2, 4, 1, 6, 0, 9, 0, 2, 0, 11, 0, 2, 0, 7, 0, 11, 1, 4, 0, 2, 0, 11, 0, 3, 1, 8, 0, 6, 0, 7

Offset

1,4

Comments

For more information see A237270.

Links

Antti Karttunen, Table of n, a(n) for n = 1..5000 (computed from the b-file of A237271 provided by Michel Marcus)

Formula

a(n) = A000005(n) - A237271(n).

Example

For n = 9 the divisors of 9 are [1, 3, 9] and the parts of the symmetric representation of sigma(9) are [5, 3, 5]. In both cases there are three elements, so a(9) = 3 - 3 = 0.
For n = 10 the four divisors of 10 are [1, 2, 5, 10] and the two parts of the symmetric representation of sigma(10) are [9, 9], so a(10) = 4 - 2 = 2.

Mathematica

(* Function a237270[] is defined in A237270 *)
a243982[n_]:=Length[Divisors[n] - Length[a237270[n]]
a243982[m_, n_]:=Map[a243982, Range[m, n]]
a243982[1, 104]] (* data *)
(* Hartmut F. W. Hoft, Sep 19 2014 *)

Crossrefs

Cf. A000005, A000203, A071561, A071562, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239657, A239660, A239931-A239934.

Sequence in context: A298645 A243319 A189230 * A214000 A161123 A035442

Adjacent sequences: A243979 A243980 A243981 * A243983 A243984 A243985

Keyword

nonn

Author

Omar E. Pol, Jun 16 2014

Extensions

a(94)-a(95) corrected by Omar E. Pol, Jul 02 2014

Status

approved