login
A333771
Triangular numbers that are the product of four distinct primes.
2
210, 1326, 1770, 1830, 2145, 2346, 2415, 2926, 3003, 3486, 4186, 4278, 5565, 6105, 6555, 6670, 7626, 8385, 8646, 9730, 11935, 12246, 13695, 16653, 17205, 17391, 17578, 18915, 22155, 22578, 24531, 25878, 26106, 27730, 27966, 28203, 30381, 32385, 33411, 35245
OFFSET
1,1
COMMENTS
The maximum exponent for each prime in the factorization of each term is one. - Harvey P. Dale, Jul 21 2021
LINKS
EXAMPLE
The 20th triangular number, T(20) = 20*21/2 = 210 = 2 * 3 * 5 * 7, so 210 is a term.
T(1333) = 889111 = 23 * 29 * 31 * 43, so 889111 is a term.
MAPLE
q:= n-> map(i-> i[2], ifactors(n)[2])=[1$4]:
select(q, [seq(n*(n+1)/2, n=0..300)])[]; # Alois P. Heinz, Apr 04 2020
MATHEMATICA
Select[Accumulate[Range[300]], PrimeNu[#]==PrimeOmega[#]==4&] (* Harvey P. Dale, Jul 21 2021 *)
CROSSREFS
Cf. A000217 (triangular numbers), A068443 (triangular numbers that are the product of 2 distinct primes), A128896 (triangular numbers that are the product of 3 distinct primes).
Sequence in context: A217532 A289319 A157408 * A118281 A328762 A047633
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Apr 04 2020
STATUS
approved