OFFSET
0,2
LINKS
Sebastian Karlsson, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Distinct Prime Factors
FORMULA
a(n) = 1 + Sum_{k=1..n} 2^A334655(k). - Sebastian Karlsson, Feb 18 2021
EXAMPLE
a(5) = 17 subsets: {}, {1}, {2}, {3}, {4}, {5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}, {3, 5}, {4, 5}, {2, 3, 4}, {2, 3, 5}, {2, 4, 5}, {3, 4, 5} and {2, 3, 4, 5}.
PROG
(Python)
from sympy import primefactors
def test(n):
if n==0: return -1
return len(primefactors(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(43)]) # Michael S. Branicky, Dec 07 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 07 2020
EXTENSIONS
a(23)-a(42) from Michael S. Branicky, Dec 07 2020
STATUS
approved