A236103 Number of distinct partition numbers dividing n.

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

Offset

1,2

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Formula

From Amiram Eldar, Jan 01 2024: (Start)

a(n) = Sum_{d|n} A167392(d).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A078506 = 2.510597... . (End)

Example

For n = 20 the divisors of 20 are 1, 2, 4, 5, 10, 20 and three of them are also partition numbers: 1, 2, 5, so a(20) = 3.
For n = 42 the divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42 and five of them are also partition numbers: 1, 2, 3, 7, 42, so a(42) = 5.

Mathematica

p = {1}; Table[If[n >= Last@p, AppendTo[p, PartitionsP[1 + Length@p]]]; Length@Select[p, Mod[n, #] == 0 &], {n, 90}] (* Giovanni Resta, Jan 22 2014 *)

Crossrefs

Cf. A000041, A001221, A049575, A078506, A085543, A167392, A236102, A236105, A236107, A236108.

Sequence in context: A259651 A253719 A081147 * A278293 A163671 A287841

Adjacent sequences: A236100 A236101 A236102 * A236104 A236105 A236106

Keyword

nonn

Author

Omar E. Pol, Jan 21 2014

Status

approved