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 A324737 Number of subsets of {2...n} containing every element of {2...n} whose prime indices all belong to the subset. 8
 1, 2, 3, 6, 8, 16, 24, 48, 84, 168, 216, 432, 648, 1296, 2448, 4896, 6528, 13056, 19584, 39168, 77760, 155520, 229248, 458496, 790272, 1580544, 3128832, 6257664, 9386496, 18772992, 24081408, 48162816, 95938560, 191877120, 378335232, 756670464, 1135005696, 2270011392 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. Also the number of subsets of {2...n} with complement containing no term whose prime indices all belong to the subset. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..100 EXAMPLE The a(1) = 1 through a(6) = 16 subsets:   {}  {}   {}     {}       {}         {}       {2}  {3}    {3}      {4}        {4}            {2,3}  {4}      {5}        {5}                   {2,3}    {3,5}      {6}                   {3,4}    {4,5}      {3,5}                   {2,3,4}  {2,3,5}    {4,5}                            {3,4,5}    {4,6}                            {2,3,4,5}  {5,6}                                       {2,3,5}                                       {3,4,5}                                       {3,5,6}                                       {4,5,6}                                       {2,3,4,5}                                       {2,3,5,6}                                       {3,4,5,6}                                       {2,3,4,5,6} An example for n = 15 is {2, 3, 5, 8, 9, 10, 11, 15}. The numbers from 2 to 15 with all prime indices in the subset are {3, 5, 9, 11, 15}, which all belong to the subset, as required. MATHEMATICA Table[Length[Select[Subsets[Range[2, n]], Function[set, SubsetQ[set, Select[Range[2, n], SubsetQ[set, PrimePi/@First/@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])); ((k, b)->if(k>#p, 1, my(t=self()(k+1, b+(1<

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Last modified February 19 09:33 EST 2020. Contains 332041 sequences. (Running on oeis4.)