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A348538
Number of partitions of n into 3 parts whose smallest part divides n.
1
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
1,5
FORMULA
a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - ceiling(n/j) + floor(n/j)).
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 *)
CROSSREFS
Cf. A069905.
Sequence in context: A112823 A247176 A325163 * A185075 A342693 A349338
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 21 2021
STATUS
approved