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

Author

Omar E. Pol, Jun 16 2014

Keywords

• nonn

Comments

Conjecture: a(n) is the number of divisors r of n such that r is not greater than twice the adjacent previous divisor of n. - Omar E. Pol, Aug 04 2025

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

Formula

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

Extensions

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