A325861 - OEIS

A325861

Number of maximal subsets of {1..n} such that every pair of distinct elements has a different quotient.

1, 1, 1, 1, 3, 3, 6, 6, 9, 13, 32, 32, 57, 57, 140, 229, 373, 373, 549, 549, 825, 1343, 3085, 3085, 4963, 6046, 13964, 20096, 28668, 28668, 42836, 42836, 57000, 95696, 217848, 301576, 434776, 434776, 977208, 1700376, 2429248, 2429248, 3444196, 3444196, 4855500

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OFFSET

0,5

LINKS

Christian Sievers, Table of n, a(n) for n = 0..61

FORMULA

a(p) = a(p-1) = A325869(p) for primes p. - Christian Sievers, Oct 29 2025

EXAMPLE

The a(1) = 1 through a(9) = 13 subsets:

{1} {12} {123} {123} {1235} {1235} {12357} {23457} {24567}

{134} {1345} {1256} {12567} {24567} {123578}

{234} {2345} {2345} {23457} {123578} {134567}

{2356} {23567} {125678} {134578}

{2456} {24567} {134567} {135678}

{13456} {134567} {134578} {145678}

{135678} {145789}

{145678} {234579}

{235678} {235678}

{235789}

{345789}

{356789}

{1256789}

MATHEMATICA

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

Table[Length[fasmax[Select[Subsets[Range[n]], UnsameQ@@Divide@@@Subsets[#, {2}]&]]], {n, 0, 10}]

CROSSREFS

The subset case is A325860.

The maximal case is A325861.

The integer partition case is A325853.

The strict integer partition case is A325854.

Heinz numbers of the counterexamples are given by A325994.

Cf. A002033, A103300, A143823, A196724, A325859, A325868, A325869.

Sequence in context: A168237 A290966 A049318 * A376449 A079551 A182843

Adjacent sequences: A325858 A325859 A325860 * A325862 A325863 A325864

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 31 2019

EXTENSIONS

a(21) onwards from Christian Sievers, Oct 29 2025

STATUS

approved