OFFSET
0,3
FORMULA
a(p) = 2*a(p-1) for p prime. - Michael S. Branicky, Aug 03 2022
EXAMPLE
The a(0) = 1 through a(4) = 10 multisets:
{} {1} {1,1} {1,1,1} {1,1,1,1}
{1,2} {1,1,2} {1,1,1,2}
{1,1,3} {1,1,1,3}
{1,2,3} {1,1,1,4}
{1,1,2,2}
{1,1,2,3}
{1,1,2,4}
{1,1,3,4}
{1,2,2,3}
{1,2,3,4}
MATHEMATICA
Table[Length[Union[Sort/@Tuples[Divisors/@Range[n]]]], {n, 0, 10}]
PROG
(Python)
from sympy import divisors
from itertools import count, islice
def agen():
s = {tuple()}
for n in count(1):
yield len(s)
s = set(tuple(sorted(t+(d, ))) for t in s for d in divisors(n))
print(list(islice(agen(), 16))) # Michael S. Branicky, Aug 03 2022
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 20 2022
EXTENSIONS
a(15)-a(21) from Michael S. Branicky, Aug 03 2022
a(22)-a(23) from Michael S. Branicky, Aug 08 2022
STATUS
approved