A356095 Tetrahedral numbers which are products of three distinct primes.

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

1,1

Comments

A squarefree subsequence of tetrahedral numbers T(n) = C(n+2,3) = n*(n+1)*(n+2)/6.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

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

Mathematica

Select[Table[n*(n + 1)*(n + 2)/6, {n, 1, 2000}], FactorInteger[#][[;; , 2]] == {1, 1, 1} &] (* Amiram Eldar, Jul 26 2022 *)

Prog

(Python)
from math import comb
from itertools import count, islice
from collections import deque, Counter
from sympy import factorint
def A356095_gen(): # generator of terms
    c, d = deque([Counter(factorint(i)) for i in range(1, 4)]), Counter(factorint(6))
    for k in count(1):
        a = sum(c, start=Counter())-d
        if len(a) == 3 == sum(a.values()):
            yield comb(k+2, 3)
        c.popleft()
        c.append(Counter(factorint(k+3)))
A356095_list = list(islice(A356095_gen(), 30)) # Chai Wah Wu, May 23 2026

Crossrefs

Intersection of A000292 and A007304.

Subsequence of A070755.

Sequence in context: A319328 A301970 A176877 * A323379 A215967 A029563

Adjacent sequences: A356092 A356093 A356094 * A356096 A356097 A356098

Keyword

nonn

Author

Massimo Kofler, Jul 26 2022

Status

approved