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A326179
Number of subsets of {1..n} containing n whose product is divisible by their sum.
5
0, 1, 1, 2, 1, 5, 9, 15, 30, 65, 138, 274, 563, 1149, 2441, 5110, 9090, 19645, 37524, 79178, 156697, 324182, 663749, 1353984, 2529510, 5088926, 10686159, 19987129, 40800192, 85303150, 162549135, 341440697, 630392773, 1317158898, 2687152135, 5276362642, 10078384386, 21415439670, 43367751196, 86613992774, 166456115593
OFFSET
0,4
EXAMPLE
The a(1) = 1 through a(7) = 15 subsets:
{1} {2} {3} {4} {5} {6} {7}
{1,2,3} {1,4,5} {3,6} {1,6,7}
{2,3,5} {2,4,6} {2,5,7}
{3,4,5} {4,5,6} {3,4,7}
{1,2,3,4,5} {1,2,3,6} {3,5,7}
{1,3,5,6} {1,2,4,7}
{3,4,5,6} {2,3,6,7}
{1,2,3,4,6} {2,5,6,7}
{2,3,4,5,6} {3,5,6,7}
{1,2,5,6,7}
{1,3,4,5,7}
{1,3,4,6,7}
{2,3,4,5,7}
{2,4,5,6,7}
{1,2,3,4,5,6,7}
MATHEMATICA
Table[Length[Select[Subsets[Range[n], {1, n}], MemberQ[#, n]&&Divisible[Times@@#, Plus@@#]&]], {n, 0, 10}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 13 2019
EXTENSIONS
a(21)-a(30) from Alois P. Heinz, Jun 13 2019
a(31)-a(40) from Bert Dobbelaere, Jun 23 2019
STATUS
approved