OFFSET
0,3
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(1) = 1 through a(8) = 6 maximal subsets:
{1} {1} {2} {1,3} {1,3} {1,3,6} {3,4,6} {1,3,6,7}
{2} {1,3} {2,4} {1,5} {1,5,6} {1,3,6,7} {1,5,6,7}
{3,4} {3,4} {3,4,6} {1,5,6,7} {3,4,6,8}
{2,4,5} {2,4,5,6} {2,4,5,6} {3,6,7,8}
{2,5,6,7} {2,4,5,6,8}
{2,5,6,7,8}
MATHEMATICA
maxim[s_]:=Complement[s, Last/@Select[Tuples[s, 2], UnsameQ@@#&&SubsetQ@@#&]];
Table[Length[maxim[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]));
my(ismax(b)=for(k=1, #p, if(!bittest(b, k) && bitnegimply(p[k], b), my(e=bitor(b, 1<<k), f=0); for(j=k+1, #p, if(bittest(b, j) && !bitnegimply(p[j], e), f=1; break)); if(!f, return(0)) )); 1);
my(recurse(k, b)=if(k>#p, ismax(b), my(f=bitnegimply(p[k], b)); if(!f || bittest(d, k), self()(k+1, b)) + if(f, self()(k+1, b+(1<<k)))));
recurse(1, 0)} \\ Andrew Howroyd, Aug 27 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 15 2019
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Aug 27 2019
STATUS
approved