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 A325365 Number of maximal subsets of {1..n} containing n such that no two elements have the same sorted prime signature. 6
 1, 1, 1, 2, 1, 3, 1, 4, 4, 8, 4, 20, 4, 12, 12, 48, 8, 56, 16, 64, 48, 48, 36, 324, 162, 81, 567, 378, 168, 1680, 168, 1848, 264, 264, 264, 2640, 240, 288, 288, 3456, 576, 7488, 1152, 4032, 4032, 2016, 1872, 28080, 9360, 6240, 3360, 6720, 3584, 28672, 6144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The sorted prime signature (A118914) of a positive integer is the multiset of exponents in its standard factorization into prime numbers. LINKS FORMULA a(n) = A326439(n)/A064839(n). EXAMPLE The a(1) = 1 through a(12) = 20 subsets (A = 10, B = 11, C = 12) are the following. The common cardinality of sets in column n is A085089(n).   1  12  13  124  145  1246  1467  12468  12689  1248A  1468B  12468C              134       1346        13468  13689  1289A  148AB  1248AC                        1456        14568  15689  1348A  1689B  12689C                                    14678  16789  1389A  189AB  1289AC                                                  1458A         13468C                                                  1478A         1348AC                                                  1589A         13689C                                                  1789A         1389AC                                                                14568C                                                                1458AC                                                                14678C                                                                1468BC                                                                1478AC                                                                148ABC                                                                15689C                                                                1589AC                                                                16789C                                                                1689BC                                                                1789AC                                                                189ABC MATHEMATICA prisig[n_]:=If[n==1, {}, Sort[Last/@FactorInteger[n]]]; Table[Times@@Length/@Split[Sort[Array[prisig, n]]]/Count[Array[prisig, n], prisig[n]], {n, 30}] CROSSREFS Cf. A001221, A001222, A025487, A064839, A085089, A112798, A118914, A124010, A181819, A324762, A325263, A325365, A326438, A326441. Sequence in context: A278575 A175126 A142884 * A177687 A219356 A142878 Adjacent sequences:  A325362 A325363 A325364 * A325366 A325367 A325368 KEYWORD nonn AUTHOR Gus Wiseman, Jul 06 2019 STATUS approved

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Last modified December 5 17:42 EST 2019. Contains 329768 sequences. (Running on oeis4.)