%I #13 Jun 11 2022 19:10:23
%S 1,3,21,36,105,231,666,2080,2346,4186,5356,5886,6903,7140,7503,7875,
%T 9730,10296,16836,20301,21945,26106,28680,29646,33930,43660,46360,
%U 51040,52003,55611,57970,59340,79800,81810,85078,91806,95266,98790
%N Triangular numbers whose sum of prime factors (with repetition) is also triangular.
%H Amiram Eldar, <a href="/A076169/b076169.txt">Table of n, a(n) for n = 1..10000</a>
%e 21 = 3 * 7 is a term since it is a triangular number, and 3 + 7 = 10 is also a triangular number.
%t triQ[n_] := IntegerQ @ Sqrt[1 + 8 * Plus @@ Times @@@ FactorInteger[n]]; tri[n_] = n*(n + 1)/2; Select[tri /@ Range[500], triQ] (* _Amiram Eldar_, Dec 11 2019 *)
%t Module[{nn=500,trs},trs=Accumulate[Range[nn]];Select[trs,MemberQ[trs,Total[ Times@@@ FactorInteger[#]]]&]] (* _Harvey P. Dale_, Jun 11 2022 *)
%Y Cf. A000217, A001414.
%K nonn
%O 1,2
%A _Jason Earls_, Nov 01 2002