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A326156
Number of nonempty subsets of {1..n} whose product is divisible by their sum.
13
0, 1, 2, 4, 5, 10, 19, 34, 64, 129, 267, 541, 1104, 2253, 4694, 9804, 18894, 38539, 76063, 155241, 311938, 636120, 1299869, 2653853, 5183363, 10272289, 20958448, 40945577, 81745769, 167048919, 329598054, 671038751, 1301431524, 2618590422, 5305742557, 10582105199, 20660489585, 42075929255, 85443680451, 172057673225, 338513788818
OFFSET
0,3
EXAMPLE
The a(1) = 1 through a(6) = 19 subsets:
{1} {1} {1} {1} {1} {1}
{2} {2} {2} {2} {2}
{3} {3} {3} {3}
{1,2,3} {4} {4} {4}
{1,2,3} {5} {5}
{1,2,3} {6}
{1,4,5} {3,6}
{2,3,5} {1,2,3}
{3,4,5} {1,4,5}
{1,2,3,4,5} {2,3,5}
{2,4,6}
{3,4,5}
{4,5,6}
{1,2,3,6}
{1,3,5,6}
{3,4,5,6}
{1,2,3,4,5}
{1,2,3,4,6}
{2,3,4,5,6}
MATHEMATICA
Table[Length[Select[Subsets[Range[n], {1, n}], Divisible[Times@@#, Plus@@#]&]], {n, 0, 10}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 11 2019
EXTENSIONS
a(21)-a(30) from Alois P. Heinz, Jun 13 2019
a(31)-a(40) from Bert Dobbelaere, Jun 22 2019
STATUS
approved