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A353027
Tetrahedral (or triangular pyramidal) numbers which are products of four distinct primes.
2
1330, 6545, 16215, 23426, 35990, 39711, 47905, 52394, 57155, 79079, 105995, 138415, 198485, 221815, 246905, 366145, 477191, 762355, 1004731, 1216865, 1293699, 1373701, 1587986, 1633355, 1726669, 1823471, 1975354, 2246839, 2862209, 2997411, 3208094, 3580779, 4149466, 4590551
OFFSET
1,1
COMMENTS
A squarefree subsequence of tetrahedral numbers.
LINKS
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
Intersection of A000292 and A046386.
Subsequence of A070755.
Sequence in context: A205091 A038854 A323329 * A182371 A252258 A038677
KEYWORD
nonn
AUTHOR
Massimo Kofler, Apr 18 2022
STATUS
approved