login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers that can be written as a product of distinct triangular numbers.
2

%I #7 Apr 21 2020 19:49:56

%S 0,1,3,6,10,15,18,21,28,30,36,45,55,60,63,66,78,84,90,91,105,108,120,

%T 126,135,136,150,153,165,168,171,180,190,198,210,216,231,234,253,270,

%U 273,276,280,300,315,325,330,351,360,378,396,406,408,420,435,450

%N Numbers that can be written as a product of distinct triangular numbers.

%H Robert Israel, <a href="/A334130/b334130.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangularNumber.html">Triangular Number</a>

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

%p N:= 1000: # for all terms <= N

%p S:= {0,1}:

%p for i from 2 do

%p t:= i*(i+1)/2;

%p if t > N then break fi;

%p S:= S union select(`<=`,map(`*`,S,t),N)

%p od:

%p sort(convert(S,list)); # _Robert Israel_, Apr 21 2020

%Y Cf. A000217, A006472, A054731, A085780, A085782, A334129.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Apr 14 2020