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

Author

Jon E. Schoenfield, Apr 04 2020

Keywords

• nonn

Comments

The maximum exponent for each prime in the factorization of each term is one. - Harvey P. Dale, Jul 21 2021

Examples

			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.
		

Links

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

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.

Programs

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 *)