A121479 -id:A121479 - cp's OEIS frontend

A121478 Triangular numbers with three distinct prime factors.

66, 78, 105, 120, 190, 231, 276, 300, 378, 406, 435, 465, 528, 561, 595, 666, 741, 820, 861, 903, 946, 1035, 1128, 1176, 1275, 1378, 1485, 1653, 1953, 2016, 2080, 2211, 2278, 2485, 2556, 2628, 2775, 3081, 3160, 3240, 3655, 3741, 3916, 4005, 4371, 4465

Offset: 1

Klaus Brockhaus, Aug 01 2006

			11*12/2 = 2*3*11 = 66 is the smalles triangular number with three distinct prime factors, hence a(1) = 66.

Cf. A000217, A068443, A119663, A121479.

Select[Accumulate[Range[0, 100]] ,PrimeNu[#]==3&] (* James C. McMahon, Oct 19 2024 *)

for(n=1,100,k=binomial(n+1,2);if(omega(k)==3,print1(k,",")))

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

Original entry on oeis.org

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

Jon E. Schoenfield, Apr 04 2020

nonn

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

			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.

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

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.

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

Select[Accumulate[Range[300]],PrimeNu[#]==PrimeOmega[#]==4&] (* Harvey P. Dale, Jul 21 2021 *)

cp's OEIS Frontend

A121478 Triangular numbers with three distinct prime factors.

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