OFFSET
0,3
FORMULA
a(p) = 2 * a(p-1) for prime p. - David A. Corneth, Feb 25 2024
a(n) = 2^n - A370583(n).
EXAMPLE
The a(0) = 1 through a(6) = 20 subsets:
{} {} {} {} {} {} {}
{2} {2} {2} {2} {2}
{3} {3} {3} {3}
{2,3} {4} {4} {4}
{2,3} {5} {5}
{3,4} {2,3} {6}
{2,5} {2,3}
{3,4} {2,5}
{3,5} {2,6}
{4,5} {3,4}
{2,3,5} {3,5}
{3,4,5} {3,6}
{4,5}
{4,6}
{5,6}
{2,3,5}
{2,5,6}
{3,4,5}
{3,5,6}
{4,5,6}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], Length[Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]>0&]], {n, 0, 10}]
CROSSREFS
The complement is counted by A370583.
For a unique choice we have A370584.
The maximal case is A370585.
A307984 counts Q-bases of logarithms of positive integers.
A355741 counts choices of a prime factor of each prime index.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 25 2024
EXTENSIONS
a(19) from David A. Corneth, Feb 25 2024
a(20)-a(41) from Alois P. Heinz, Feb 25 2024
STATUS
approved