%I #26 Apr 20 2023 02:29:27
%S 1330,6545,16215,23426,35990,39711,47905,52394,57155,79079,105995,
%T 138415,198485,221815,246905,366145,477191,762355,1004731,1216865,
%U 1293699,1373701,1587986,1633355,1726669,1823471,1975354,2246839,2862209,2997411,3208094,3580779,4149466,4590551
%N Tetrahedral (or triangular pyramidal) numbers which are products of four distinct primes.
%C A squarefree subsequence of tetrahedral numbers.
%H Robert Israel, <a href="/A353027/b353027.txt">Table of n, a(n) for n = 1..10000</a>
%e 1330 = 19*20*21/6 = 2 * 5 * 7 * 19;
%e 6545 = 33*34*35/6 = 5 * 7 * 11 * 17;
%e 16215 = 45*46*47/6 = 3 * 5 * 23 * 47;
%e 23426 = 51*52*53/6 = 2 * 13 * 17 * 53.
%p filter:= proc(n) local F;
%p F:= ifactors(n,easy)[2];
%p F[..,2] = [1,1,1,1]
%p end proc:
%p select(filter, [seq(n*(n+1)*(n+2)/6,n=1..1000)]); # _Robert Israel_, Apr 18 2023
%t Select[Table[n*(n + 1)*(n + 2)/6, {n, 1, 300}], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1} &] (* _Amiram Eldar_, Apr 18 2022 *)
%o (Python)
%o from sympy import factorint
%o from itertools import count, islice
%o def agen():
%o for t in (n*(n+1)*(n+2)//6 for n in count(1)):
%o f = factorint(t, multiple=True)
%o if len(f) == len(set(f)) == 4: yield t
%o print(list(islice(agen(), 34))) # _Michael S. Branicky_, May 28 2022
%Y Intersection of A000292 and A046386.
%Y Subsequence of A070755.
%K nonn
%O 1,1
%A _Massimo Kofler_, Apr 18 2022