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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 24 12:02 EDT 2022. Contains 356932 sequences. (Running on oeis4.)