A353027 Tetrahedral (or triangular pyramidal) numbers which are products of four distinct primes.

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

Author

Massimo Kofler, Apr 18 2022

Keywords

• nonn

Comments

A squarefree subsequence of tetrahedral numbers.

Examples

			   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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A000292 and A046386.

Subsequence of A070755.

Programs

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 *)

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