A348538 Number of partitions of n into 3 parts whose smallest part divides n.

0, 0, 1, 1, 2, 3, 3, 5, 5, 7, 5, 12, 6, 11, 12, 16, 8, 21, 9, 25, 18, 19, 11, 41, 18, 23, 24, 38, 14, 54, 15, 45, 30, 31, 36, 76, 18, 35, 36, 80, 20, 81, 21, 64, 68, 43, 23, 121, 39, 76, 48, 77, 26, 108, 60, 119, 54, 55, 29, 191, 30, 59, 101, 118, 72, 135, 33, 103, 66, 156, 35

Offset: 1

Author

Wesley Ivan Hurt, Oct 21 2021

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to partitions

Crossrefs

Cf. A069905.

Programs

Maple

f:= proc(n) local i,j;
    add((floor((n-j)/2)-j+1), j = select(`<=`, numtheory:-divisors(n),n/3))
end proc:
map(f, [$1..100]); # Robert Israel, Sep 30 2024

Mathematica

Array[Sum[Sum[(1 - Ceiling[#/j] + Floor[#/j]), {i, j, Floor[(# - j)/2]}], {j, Floor[#/3]}] &, 71] (* Michael De Vlieger, Oct 21 2021 *)
Table[Count[IntegerPartitions[n,{3}],?(Divisible[n,#[[-1]]]&)],{n,80}] (* _Harvey P. Dale, Jul 10 2022 *)

Formula

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - ceiling(n/j) + floor(n/j)).