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 A324741 Number of subsets of {1...n} containing no prime indices of the elements. 19
 1, 2, 3, 5, 8, 13, 19, 30, 54, 96, 156, 248, 440, 688, 1120, 1864, 3664, 5856, 11232, 16896, 31296, 53952, 91008, 137472, 270528, 516720, 863088, 1710816, 3173856, 4836672, 9329472, 14897376, 29788128, 52256448, 88429248, 166037184, 331648704, 497685888, 829449600 (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) = 19 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}    {2,4}                               {3,4}    {2,5}                               {4,5}    {3,4}                               {2,4,5}  {3,6}                                        {4,5}                                        {4,6}                                        {5,6}                                        {2,4,5}                                        {3,4,6}                                        {4,5,6} An example for n = 20 is {5,6,7,9,10,12,14,15,16,19,20}, with prime indices:    5: {3}    6: {1,2}    7: {4}    9: {2,2}   10: {1,3}   12: {1,1,2}   14: {1,4}   15: {2,3}   16: {1,1,1,1}   19: {8}   20: {1,1,3} None of these prime indices {1,2,3,4,8} belong to the subset, as required. MATHEMATICA Table[Length[Select[Subsets[Range[n]], Intersection[#, PrimePi/@First/@Join@@FactorInteger/@#]=={}&]], {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, 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(!bitand(p[k], b), t+=if(bittest(d, k), self()(k+1, b+(1<

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Last modified April 4 04:53 EDT 2020. Contains 333212 sequences. (Running on oeis4.)