

A076169


Triangular numbers whose sum of prime factors (with repetition) is also triangular.


1



1, 3, 21, 36, 105, 231, 666, 2080, 2346, 4186, 5356, 5886, 6903, 7140, 7503, 7875, 9730, 10296, 16836, 20301, 21945, 26106, 28680, 29646, 33930, 43660, 46360, 51040, 52003, 55611, 57970, 59340, 79800, 81810, 85078, 91806, 95266, 98790
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OFFSET

1,2


LINKS



EXAMPLE

21 = 3 * 7 is a term since it is a triangular number, and 3 + 7 = 10 is also a triangular number.


MATHEMATICA

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 *)
Module[{nn=500, trs}, trs=Accumulate[Range[nn]]; Select[trs, MemberQ[trs, Total[ Times@@@ FactorInteger[#]]]&]] (* Harvey P. Dale, Jun 11 2022 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



