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 A324738 Number of subsets of {1...n} containing no element > 1 whose prime indices all belong to the subset. 13
 1, 2, 3, 5, 8, 13, 26, 42, 72, 120, 232, 376, 752, 1128, 2256, 4512, 8256, 13632, 27264, 42048, 82944, 158976, 313344, 497664, 995328, 1700352, 3350016, 5815296, 11630592, 17491968, 34983936, 56954880, 108933120, 210788352, 418258944, 804667392, 1609334784 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..100 EXAMPLE The a(0) = 1 through a(6) = 26 subsets:   {}  {}   {}   {}     {}     {}       {}       {1}  {1}  {1}    {1}    {1}      {1}            {2}  {2}    {2}    {2}      {2}                 {3}    {3}    {3}      {3}                 {1,3}  {4}    {4}      {4}                        {1,3}  {5}      {5}                        {2,4}  {1,3}    {6}                        {3,4}  {1,5}    {1,3}                               {2,4}    {1,5}                               {2,5}    {1,6}                               {3,4}    {2,4}                               {4,5}    {2,5}                               {2,4,5}  {2,6}                                        {3,4}                                        {3,6}                                        {4,5}                                        {4,6}                                        {5,6}                                        {1,3,6}                                        {1,5,6}                                        {2,4,5}                                        {2,4,6}                                        {2,5,6}                                        {3,4,6}                                        {4,5,6}                                        {2,4,5,6} MATHEMATICA Table[Length[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])); ((k, b)->if(k>#p, 1, my(t=self()(k+1, b)); if(bitnegimply(p[k], b), t+=if(bittest(d, k), self()(k+1, b+(1<

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Last modified May 30 18:38 EDT 2020. Contains 334728 sequences. (Running on oeis4.)