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A326180 Number of maximal subsets of {1..n} containing n whose product is divisible by their sum. 5
0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 11, 1, 16, 1, 1, 1, 27, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(A060462(n)) = 1.

EXAMPLE

The a(6) = 3, a(10) = 11, and a(12) = 16 subsets:

{1,3,5,6} {1,2,4,5,6,7,10} {1,2,3,4,5,6,7,8,12}

{1,2,3,4,6} {1,2,3,4,5,7,8,10} {1,3,4,5,6,7,8,10,12}

{2,3,4,5,6} {1,2,3,4,6,7,9,10} {1,3,4,6,7,8,9,10,12}

{1,2,3,5,6,7,8,10} {1,3,4,5,6,8,10,11,12}

{1,2,3,5,7,8,9,10} {1,2,3,4,5,6,8,9,10,12}

{1,2,5,6,7,8,9,10} {1,2,3,4,6,7,8,9,11,12}

{1,3,4,5,6,7,9,10} {1,2,3,5,6,7,8,9,10,12}

{1,3,4,6,7,8,9,10} {1,2,3,5,6,7,8,9,11,12}

{1,4,5,6,7,8,9,10} {1,3,4,5,6,7,8,9,11,12}

{1,2,3,4,5,6,8,9,10} {1,2,3,4,6,7,8,10,11,12}

{2,3,4,5,6,7,8,9,10} {1,2,3,4,6,8,9,10,11,12}

{1,3,5,6,7,8,9,10,11,12}

{1,2,3,4,5,6,7,9,10,11,12}

{1,2,3,4,5,7,8,9,10,11,12}

{1,2,4,5,6,7,8,9,10,11,12}

{2,3,4,5,6,7,8,9,10,11,12}

MATHEMATICA

fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];

Table[Length[fasmax[Select[Subsets[Range[n], {1, n}], MemberQ[#, n]&&Divisible[Times@@#, Plus@@#]&]]], {n, 0, 10}]

CROSSREFS

Cf. A053632, A057567, A057568, A059529, A060462, A063865, A301987, A326153/A326154, A326156, A326158, A326178, A326179.

Sequence in context: A185620 A096066 A294746 * A064085 A256692 A228637

Adjacent sequences: A326177 A326178 A326179 * A326181 A326182 A326183

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 13 2019

STATUS

approved

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Last modified December 5 16:58 EST 2022. Contains 358588 sequences. (Running on oeis4.)