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<<k)), t)); t))(1, 0)} \\ Andrew Howroyd, Aug 16 2019
CROSSREFS
The maximal case is A324762. The case of subsets of {1...n} is A324738. The strict integer partition version is A324750. The integer partition version is A324755. The Heinz number version is A324760. An infinite version is A324694.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 14 2019
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Aug 16 2019
STATUS
approved