A326496
Number of maximal product-free subsets of {1..n}.
Original entry on oeis.org
1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 6, 6, 9, 9, 15, 17, 30, 30, 46, 46, 51, 61, 103, 103, 129, 158, 282, 282, 322, 322, 553, 553, 615, 689, 1247, 1365, 1870, 1870, 3566, 3758, 5244, 5244, 8677, 8677, 9807, 12147, 23351, 23351, 27469, 31694, 45718, 47186, 54594, 54594, 95382, 108198
Offset: 0
The a(2) = 1 through a(10) = 6 subsets (A = 10):
{2} {23} {23} {235} {235} {2357} {23578} {23578} {23578}
{34} {345} {256} {2567} {25678} {256789} {2378A}
{3456} {34567} {345678} {345678} {256789}
{456789} {26789A}
{345678A}
{456789A}
- Fausto A. C. Cariboni, Table of n, a(n) for n = 0..85
- P. J. Cameron and P. Erdős, On the number of integers with various properties, in R. A. Mullin, ed., Number Theory: Proc. First Conf. of Canad. Number Theory Assoc. Conf., Banff, De Gruyter, Berlin, 1990, pp. 61-79.
- Andrew Howroyd, PARI Program
Subsets without products of distinct elements are
A326117.
Maximal sum-free subsets are
A121269.
Maximal sum-free and product-free subsets are
A326497.
Maximal subsets without products of distinct elements are
A325710.
-
fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Times@@@Tuples[#,2]]=={}&]]],{n,0,10}]
-
\\ See link for program file.
for(n=0, 30, print1(A326496(n), ", ")) \\ Andrew Howroyd, Aug 30 2019
A326497
Number of maximal sum-free and product-free subsets of {1..n}.
Original entry on oeis.org
1, 1, 1, 1, 2, 3, 4, 6, 8, 9, 15, 21, 26, 38, 51, 69, 89, 119, 149, 197, 261, 356, 447, 601, 781, 1003, 1293, 1714, 2228, 2931, 3697, 4843, 6258, 8187, 10273, 13445, 16894, 21953, 27469, 35842, 45410, 58948, 73939, 95199, 120593, 154510, 192995, 247966, 312642
Offset: 0
The a(2) = 1 through a(10) = 15 subsets (A = 10):
{2} {23} {23} {23} {23} {237} {256} {267} {23A}
{34} {25} {256} {256} {258} {345} {345}
{345} {345} {267} {267} {357} {34A}
{456} {345} {345} {2378} {357}
{357} {357} {2569} {38A}
{4567} {2378} {2589} {2378}
{4567} {4567} {2569}
{5678} {4679} {2589}
{56789} {267A}
{269A}
{4567}
{4679}
{479A}
{56789}
{6789A}
Sum-free and product-free subsets are
A326495.
Maximal sum-free subsets are
A121269.
Maximal product-free subsets are
A326496.
Subsets with sums (and products) are
A326083.
-
fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Union[Plus@@@Tuples[#,2],Times@@@Tuples[#,2]]]=={}&]]],{n,0,10}]
-
\\ See link for program file.
for(n=0, 37, print1(A326497(n), ", ")) \\ Andrew Howroyd, Aug 30 2019
A326491
Number of maximal subsets of {1..n} containing no differences or quotients of pairs of distinct elements.
Original entry on oeis.org
1, 1, 2, 2, 3, 4, 5, 7, 9, 10, 16, 22, 27, 39, 52, 70, 90, 120, 150, 198, 262, 357, 448, 602, 782, 1004, 1294, 1715, 2229, 2932, 3698, 4844, 6259, 8188, 10274, 13446, 16895, 21954, 27470, 35843, 45411, 58949, 73940, 95200, 120594, 154511, 192996, 247967, 312643
Offset: 0
The a(1) = 1 through a(9) = 10 subsets:
{1} {1} {1} {1} {1} {1} {1} {1} {1}
{2} {2,3} {2,3} {2,3} {2,3} {2,3,7} {2,5,6} {2,6,7}
{3,4} {2,5} {2,5,6} {2,5,6} {2,5,8} {3,4,5}
{3,4,5} {3,4,5} {2,6,7} {2,6,7} {3,5,7}
{4,5,6} {3,4,5} {3,4,5} {2,3,7,8}
{3,5,7} {3,5,7} {2,5,6,9}
{4,5,6,7} {2,3,7,8} {2,5,8,9}
{4,5,6,7} {4,5,6,7}
{5,6,7,8} {4,6,7,9}
{5,6,7,8,9}
Subsets without differences or quotients are
A326490.
Subsets with differences and quotients are
A326494.
Maximal subsets without differences are
A121269Maximal subsets without quotients are
A326492.
-
fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Union[Divide@@@Reverse/@Subsets[#,{2}],Subtract@@@Reverse/@Subsets[#,{2}]]]=={}&]]],{n,0,10}]
A325710
Number of maximal subsets of {1..n} containing no products of distinct elements.
Original entry on oeis.org
1, 1, 2, 2, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 24, 28, 32, 32, 62, 62, 92, 102, 184, 184, 254, 254, 474, 506, 686, 686, 1172, 1172, 1792, 1906, 3568, 3794, 5326, 5326, 10282, 10618, 14822, 14822, 25564, 25564, 35304, 39432, 76888, 76888, 100574, 100574, 197870, 201622, 282014
Offset: 0
The a(1) = 1 through a(9) = 6 maximal subsets:
{1} {1} {1} {1} {1} {1} {1} {1} {1}
{2} {23} {234} {2345} {2345} {23457} {23457} {234579}
{2456} {24567} {23578} {235789}
{3456} {34567} {24567} {245679}
{25678} {256789}
{345678} {3456789}
Subsets without products of distinct elements are
A326117.
Maximal product-free subsets are
A326496.
Maximal subsets without sums of distinct elements are
A326498.
Maximal subsets without quotients are
A326492.
Maximal subsets without sums or products of distinct elements are
A326025.
-
fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Times@@@Subsets[#,{2,n}]]=={}&]]],{n,0,10}]
-
\\ See link for program file.
for(n=0, 30, print1(A325710(n), ", ")) \\ Andrew Howroyd, Aug 29 2019
A327591
Number of subsets of {1..n} containing no quotients of pairs of distinct elements.
Original entry on oeis.org
1, 2, 3, 5, 7, 13, 23, 45, 89, 137, 253, 505, 897, 1793, 3393, 6353, 9721, 19441, 35665, 71329, 129953, 247233, 477665, 955329, 1700417, 2657281, 5184001, 10368001, 19407361, 38814721, 68868353, 137736705, 260693505, 505830401, 999641601, 1882820609, 2807196673
Offset: 0
The a(0) = 1 through a(5) = 13 subsets:
{} {} {} {} {} {}
{1} {1} {1} {1} {1}
{2} {2} {2} {2}
{3} {3} {3}
{2,3} {4} {4}
{2,3} {5}
{3,4} {2,3}
{2,5}
{3,4}
{3,5}
{4,5}
{2,3,5}
{3,4,5}
Maximal subsets without quotients are
A326492.
Subsets with quotients are
A326023.
Subsets without differences or quotients are
A326490.
Subsets without products are
A326489.
Showing 1-5 of 5 results.
Comments