A326179 Number of subsets of {1..n} containing n whose product is divisible by their sum.

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

Links

Table of n, a(n) for n=0..40.

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}]

Crossrefs

Cf. A053632, A057567, A057568, A059529, A063865, A301987, A326153/A326154, A326156, A326158, A326178, A326180.

Sequence in context: A021467 A011132 A178627 * A247368 A019098 A333829

Adjacent sequences: A326176 A326177 A326178 * A326180 A326181 A326182

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