A333771 Triangular numbers that are the product of four distinct primes.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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).

Cf. A076578, A121479.

Sequence in context: A217532 A289319 A157408 * A118281 A328762 A047633

Adjacent sequences: A333768 A333769 A333770 * A333772 A333773 A333774

Keyword

nonn

Author

Jon E. Schoenfield, Apr 04 2020

Status

approved