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 A324744 Number of maximal subsets of {1...n} containing no element whose prime indices all belong to the subset. 15
 1, 1, 2, 2, 3, 4, 4, 5, 6, 8, 8, 11, 11, 22, 22, 22, 22, 28, 28, 44, 44, 52, 52, 76, 76, 88, 88, 96, 96, 184, 184, 240, 240, 264, 264, 296, 296, 592, 592, 592, 592, 728, 728, 1456, 1456, 1456, 1456, 2912, 2912, 3168, 3168, 3168, 3168, 5568, 5568, 5568, 5568 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..100 EXAMPLE The a(1) = 1 through a(8) = 6 maximal subsets:   {1}  {1}  {2}    {1,3}  {1,3}    {1,3,6}    {3,4,6}    {1,3,6,7}        {2}  {1,3}  {2,4}  {1,5}    {1,5,6}    {1,3,6,7}  {1,5,6,7}                    {3,4}  {3,4}    {3,4,6}    {1,5,6,7}  {3,4,6,8}                           {2,4,5}  {2,4,5,6}  {2,4,5,6}  {3,6,7,8}                                               {2,5,6,7}  {2,4,5,6,8}                                                          {2,5,6,7,8} MATHEMATICA maxim[s_]:=Complement[s, Last/@Select[Tuples[s, 2], UnsameQ@@#&&SubsetQ@@#&]]; Table[Length[maxim[Select[Subsets[Range[n]], !MemberQ[#, k_/; SubsetQ[#, PrimePi/@First/@FactorInteger[k]]]&]]], {n, 0, 10}] PROG (PARI) pset(n)={my(b=0, f=factor(n)[, 1]); sum(i=1, #f, 1<<(primepi(f[i])))} a(n)={my(p=vector(n, k, if(k==1, 1, pset(k))), d=0); for(i=1, #p, d=bitor(d, p[i])); my(ismax(b)=for(k=1, #p, if(!bittest(b, k) && bitnegimply(p[k], b), my(e=bitor(b, 1<#p, ismax(b), my(f=bitnegimply(p[k], b)); if(!f || bittest(d, k), self()(k+1, b)) + if(f, self()(k+1, b+(1<

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Last modified July 29 06:21 EDT 2021. Contains 346340 sequences. (Running on oeis4.)