OFFSET
1,1
COMMENTS
A squarefree subsequence of tetrahedral numbers.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
1330 = 19*20*21/6 = 2 * 5 * 7 * 19;
6545 = 33*34*35/6 = 5 * 7 * 11 * 17;
16215 = 45*46*47/6 = 3 * 5 * 23 * 47;
23426 = 51*52*53/6 = 2 * 13 * 17 * 53.
MAPLE
filter:= proc(n) local F;
F:= ifactors(n, easy)[2];
F[.., 2] = [1, 1, 1, 1]
end proc:
select(filter, [seq(n*(n+1)*(n+2)/6, n=1..1000)]); # Robert Israel, Apr 18 2023
MATHEMATICA
Select[Table[n*(n + 1)*(n + 2)/6, {n, 1, 300}], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1} &] (* Amiram Eldar, Apr 18 2022 *)
PROG
(Python)
from sympy import factorint
from itertools import count, islice
def agen():
for t in (n*(n+1)*(n+2)//6 for n in count(1)):
f = factorint(t, multiple=True)
if len(f) == len(set(f)) == 4: yield t
print(list(islice(agen(), 34))) # Michael S. Branicky, May 28 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Massimo Kofler, Apr 18 2022
STATUS
approved