OFFSET
0,2
LINKS
Sebastian Karlsson, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Prime Factor
FORMULA
a(n) = 1 + Sum_{k=1..n} 2^A335097(k). - Sebastian Karlsson, Feb 23 2021
EXAMPLE
a(6) = 12 subsets: {}, {1}, {2}, {3}, {4}, {5}, {6}, {2, 3}, {2, 5}, {3, 5}, {4, 6} and {2, 3, 5}.
MATHEMATICA
Array[Count[Subsets@ Range[#], _?(SameQ @@ PrimeOmega[#] &)] &, 16, 0] (* Michael De Vlieger, Feb 24 2021 *)
PROG
(Python)
from sympy import primeomega
def test(n):
if n<2: return n-1
return primeomega(n)
def a(n):
tests = [test(i) for i in range(n+1)]
return sum(2**tests.count(v)-1 for v in set(tests))
print([a(n) for n in range(60)]) # Michael S. Branicky, Dec 07 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 07 2020
EXTENSIONS
a(25)-a(48) from Michael S. Branicky, Dec 07 2020
STATUS
approved