A357590 Triangular numbers which are products of five distinct primes.

3570, 8778, 9870, 12090, 13530, 20706, 20910, 21945, 24090, 24310, 26565, 33670, 40470, 40755, 47586, 54285, 57630, 57970, 63546, 66430, 69006, 72390, 76245, 87990, 88410, 91806, 92235, 94395, 94830, 98790, 121278, 130305, 132870, 133386, 141778, 148785, 154290, 159330, 163878, 167910

Offset: 1

Author

Massimo Kofler, Oct 05 2022

Keywords

• nonn

Comments

A squarefree subsequence of triangular numbers (T(n) = n*(n+1)/2).

Examples

			3570 = 2*3*5*7*17 = 84*85/2.
21945 = 3*5*7*11*19 = 209*210/2.
121278 = 2*3*17*29*41 = 492*493/2.
154290 = 2*3*5*37*139 = 555*556/2.
		

Crossrefs

Intersection of A000217 and A046387.

Cf. A068443, A128896, A333771.

Programs

Maple

q:= n-> map(i-> i[2], ifactors(n)[2])=[1$5]:
select(q, [seq(n*(n+1)/2, n=0..1000)])[];  # Alois P. Heinz, Oct 05 2022

Mathematica

Select[Accumulate @ Range[600], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1, 1} &] (* Amiram Eldar, Oct 05 2022 *)