A357590 Triangular numbers which are products of five distinct primes (or pentaprimes).

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

1,1

Comments

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

Links

Table of n, a(n) for n=1..40.

Example

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.

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 *)

Crossrefs

Intersection of A000217 and A046387.

Cf. A068443, A128896, A333771.

Sequence in context: A204600 A204599 A206090 * A071144 A204417 A204410

Adjacent sequences: A357587 A357588 A357589 * A357591 A357592 A357593

Keyword

nonn

Author

Massimo Kofler, Oct 05 2022

Status

approved