OFFSET
1,6
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..75
FORMULA
a(p) = a(p-1) for p prime. - Michael S. Branicky, Aug 03 2022
EXAMPLE
The a(n) multisets for n = 2, 6, 10, 12:
{1} {1,1,1,2,3} {1,1,1,1,1,2,2,3,4} {1,1,1,1,1,1,2,2,3,4,5}
{1,1,2,2,3} {1,1,1,1,2,2,2,3,4} {1,1,1,1,1,2,2,2,3,4,5}
{1,1,1,1,2,2,3,3,4} {1,1,1,1,1,2,2,3,3,4,5}
{1,1,1,2,2,2,3,3,4} {1,1,1,1,2,2,2,2,3,4,5}
{1,1,1,1,2,2,2,3,3,4,5}
{1,1,1,2,2,2,2,3,3,4,5}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[Union[Sort/@Tuples[primeMS/@Range[2, n]]]], {n, 15}]
PROG
(Python)
from sympy import factorint
from itertools import count, islice
def agen():
s = {(1, )}
for n in count(2):
yield len(s)
s = set(tuple(sorted(t+(d, ))) for t in s for d in factorint(n))
print(list(islice(agen(), 53))) # Michael S. Branicky, Aug 03 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 20 2022
EXTENSIONS
a(28) and beyond from Michael S. Branicky, Aug 03 2022
STATUS
approved