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

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