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

%I A348538 #12 Sep 30 2024 12:26:48
%S A348538 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,
%T A348538 38,14,54,15,45,30,31,36,76,18,35,36,80,20,81,21,64,68,43,23,121,39,
%U A348538 76,48,77,26,108,60,119,54,55,29,191,30,59,101,118,72,135,33,103,66,156,35
%N A348538 Number of partitions of n into 3 parts whose smallest part divides n.
%H A348538 Robert Israel, <a href="/A348538/b348538.txt">Table of n, a(n) for n = 1..10000</a>
%H A348538 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A348538 a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - ceiling(n/j) + floor(n/j)).
%p A348538 f:= proc(n) local i,j;
%p A348538     add((floor((n-j)/2)-j+1), j = select(`<=`, numtheory:-divisors(n),n/3))
%p A348538 end proc:
%p A348538 map(f, [$1..100]); # _Robert Israel_, Sep 30 2024
%t A348538 Array[Sum[Sum[(1 - Ceiling[#/j] + Floor[#/j]), {i, j, Floor[(# - j)/2]}], {j, Floor[#/3]}] &, 71] (* _Michael De Vlieger_, Oct 21 2021 *)
%t A348538 Table[Count[IntegerPartitions[n,{3}],_?(Divisible[n,#[[-1]]]&)],{n,80}] (* _Harvey P. Dale_, Jul 10 2022 *)
%Y A348538 Cf. A069905.
%K A348538 nonn
%O A348538 1,5
%A A348538 _Wesley Ivan Hurt_, Oct 21 2021