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 A324739 Number of subsets of {2...n} containing no element whose prime indices all belong to the subset. 6
 1, 2, 3, 6, 10, 20, 30, 60, 96, 192, 312, 624, 936, 1872, 3744, 7488, 12480, 24960, 37440, 74880, 142848, 285696, 456192, 912384, 1548288, 3096576, 5308416, 10616832, 15925248, 31850496, 51978240, 103956480, 200835072, 401670144, 771489792, 1542979584, 2314469376 (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. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..100 EXAMPLE The a(1) = 1 through a(6) = 20 subsets: {} {} {} {} {} {} {2} {2} {2} {2} {2} {3} {3} {3} {3} {4} {4} {4} {2,4} {5} {5} {3,4} {2,4} {6} {2,5} {2,4} {3,4} {2,5} {4,5} {2,6} {2,4,5} {3,4} {3,6} {4,5} {4,6} {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[2, n]], !MemberQ[#, k_/; SubsetQ[#, PrimePi/@First/@FactorInteger[k]]]&]], {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, 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(bitnegimply(p[k], b), t+=if(bittest(d, k), self()(k+1, b+(1<

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Last modified June 19 11:49 EDT 2024. Contains 373503 sequences. (Running on oeis4.)