This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A324736 #16 Aug 22 2019 08:24:28
%S A324736 1,2,3,4,7,9,15,22,43,79,127,175,343,511,851,1571,3141,4397,8765,
%T A324736 13147,25243,46843,76795,115171,230299,454939,758203,1516363,2916079,
%U A324736 4356079,8676079,12132079,24264157,45000157,73800253,145685053,291369853,437054653,728424421
%N A324736 Number of subsets of {1...n} containing all prime indices of the elements.
%C A324736 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.
%C A324736 Also the number of subsets of {1...n} containing no prime indices of the non-elements up to n.
%H A324736 Andrew Howroyd, <a href="/A324736/b324736.txt">Table of n, a(n) for n = 0..100</a>
%e A324736 The a(0) = 1 through a(6) = 15 subsets:
%e A324736 {} {} {} {} {} {} {}
%e A324736 {1} {1} {1} {1} {1} {1}
%e A324736 {1,2} {1,2} {1,2} {1,2} {1,2}
%e A324736 {1,2,3} {1,4} {1,4} {1,4}
%e A324736 {1,2,3} {1,2,3} {1,2,3}
%e A324736 {1,2,4} {1,2,4} {1,2,4}
%e A324736 {1,2,3,4} {1,2,3,4} {1,2,6}
%e A324736 {1,2,3,5} {1,2,3,4}
%e A324736 {1,2,3,4,5} {1,2,3,5}
%e A324736 {1,2,3,6}
%e A324736 {1,2,4,6}
%e A324736 {1,2,3,4,5}
%e A324736 {1,2,3,4,6}
%e A324736 {1,2,3,5,6}
%e A324736 {1,2,3,4,5,6}
%e A324736 An example for n = 18 is {1,2,4,7,8,9,12,16,17,18}, whose elements have the following prime indices:
%e A324736 1: {}
%e A324736 2: {1}
%e A324736 4: {1,1}
%e A324736 7: {4}
%e A324736 8: {1,1,1}
%e A324736 9: {2,2}
%e A324736 12: {1,1,2}
%e A324736 16: {1,1,1,1}
%e A324736 17: {7}
%e A324736 18: {1,2,2}
%e A324736 All of these prime indices {1,2,4,7} belong to the subset, as required.
%t A324736 Table[Length[Select[Subsets[Range[n]],SubsetQ[#,PrimePi/@First/@Join@@FactorInteger/@DeleteCases[#,1]]&]],{n,0,10}]
%o A324736 (PARI)
%o A324736 pset(n)={my(b=0, f=factor(n)[,1]); sum(i=1, #f, 1<<(primepi(f[i])))}
%o A324736 a(n)={my(p=vector(n,k,pset(k)), d=0); for(i=1, #p, d=bitor(d, p[i]));
%o A324736 ((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<<k)), t)); t))(1,0)} \\ _Andrew Howroyd_, Aug 15 2019
%Y A324736 The strict integer partition version is A324748. The integer partition version is A324753. The Heinz number version is A290822. An infinite version is A324698.
%Y A324736 Cf. A000720, A001462, A007097, A076078, A084422, A085945, A112798, A276625, A279861, A290689, A304360, A320426.
%Y A324736 Cf. A324697, A324737, A324741, A324743.
%K A324736 nonn
%O A324736 0,2
%A A324736 _Gus Wiseman_, Mar 13 2019
%E A324736 Terms a(21) and beyond from _Andrew Howroyd_, Aug 15 2019