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 A324763 Number of maximal subsets of {2...n} containing no prime indices of the elements. 10
 1, 1, 2, 2, 2, 3, 6, 6, 6, 6, 10, 10, 16, 16, 16, 16, 24, 24, 48, 48, 48, 48, 84, 84, 84, 84, 84, 84, 144, 144, 228, 228, 228, 228, 228, 228, 420, 420, 420, 420, 648, 648, 1080, 1080, 1080, 1080, 1800, 1800, 1800, 1800, 1800, 1800, 3600, 3600, 3600, 3600, 3600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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 = 1..100 EXAMPLE The a(1) = 1 through a(9) = 6 subsets:   {}  {2}  {2}  {2,4}  {3,4}    {2,4,5}  {2,4,5}  {2,4,5,8}  {2,4,5,8}            {3}  {3,4}  {2,4,5}  {3,4,6}  {2,5,7}  {2,5,7,8}  {2,5,7,8}                                 {4,5,6}  {3,4,6}  {3,4,6,8}  {3,4,6,8,9}                                          {3,6,7}  {3,6,7,8}  {3,6,7,8,9}                                          {4,5,6}  {4,5,6,8}  {4,5,6,8,9}                                          {5,6,7}  {5,6,7,8}  {5,6,7,8,9} MATHEMATICA maxim[s_]:=Complement[s, Last/@Select[Tuples[s, 2], UnsameQ@@#&&SubsetQ@@#&]]; Table[Length[maxim[Select[Subsets[Range[2, n]], Intersection[#, PrimePi/@First/@Join@@FactorInteger/@#]=={}&]]], {n, 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-1, k, pset(k+1)>>1), d=0); for(i=1, #p, d=bitor(d, p[i])); my(ismax(b)=my(e=0); forstep(k=#p, 1, -1, if(bittest(b, k), e=bitor(e, p[k]), if(!bittest(e, k) && !bitand(p[k], b), return(0)) )); 1); ((k, b)->if(k>#p, ismax(b), my(f=!bitand(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 28 22:39 EDT 2021. Contains 346338 sequences. (Running on oeis4.)