A353027
Tetrahedral (or triangular pyramidal) numbers which are products of four distinct primes.
Original entry on oeis.org
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
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.
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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
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Select[Table[n*(n + 1)*(n + 2)/6, {n, 1, 300}], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1} &] (* Amiram Eldar, Apr 18 2022 *)
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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
A354976
Squarefree tetrahedral numbers which are products of five distinct primes.
Original entry on oeis.org
7770, 14190, 98770, 121485, 129766, 273819, 383306, 457310, 632710, 735130, 848046, 971970, 1072445, 1456935, 1543465, 2027795, 2135445, 2190670, 2731135, 3136805, 3817670, 4775385, 4869634, 5159805, 5564321, 5989445, 6099006, 6209895, 8579746, 9145270, 9735114, 9886435
Offset: 1
7770 = 35*36*37/6 = 2*3*5*7*37
14190 = 43*44*45/6 = 2*3*5*11*43
98770 = 83*84*85/6 = 2*5*7*17*83
121485 = 89*90*91/6 = 3*5*7*13*89
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q:= n-> is(map(x-> x[2], ifactors(n)[2])=[1$5]):
select(q, [n*(n+1)*(n+2)/6$n=1..500])[]; # Alois P. Heinz, Jun 15 2022
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Select[Table[n*(n+1)*(n+2)/6, {n, 1, 400}], FactorInteger[#][[;;, 2]] == {1, 1, 1, 1, 1} &] (* Amiram Eldar, Jun 15 2022 *)
Select[Binomial[Range[500]+2,3],PrimeNu[#]==PrimeOmega[#]==5&] (* Harvey P. Dale, Jul 05 2025 *)
A356095
Tetrahedral numbers which are products of three distinct primes.
Original entry on oeis.org
165, 286, 455, 969, 1771, 4495, 9139, 12341, 32509, 176851, 437989, 657359, 939929, 3737581, 9290431, 21084251, 26536591, 39338069, 44101441, 61690919, 92568571, 112805879, 289442201, 381588019, 439918931, 495593039, 711215371, 815946449, 1008077071, 1103914379
Offset: 1
165 = 9*10*11/6 = 3*5*11
286 = 11*12*13/6 = 2*11*13
455 = 13*14*15/6 = 5*7*13
9139 = 37*38*39/6 = 13*19*37
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Select[Table[n*(n + 1)*(n + 2)/6, {n, 1, 2000}], FactorInteger[#][[;; , 2]] == {1, 1, 1} &] (* Amiram Eldar, Jul 26 2022 *)
Showing 1-3 of 3 results.
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