A076169 - OEIS

A076169

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A000217, A001414.

Sequence in context: A087690 A191763 A227241 * A298035 A178082 A056387

Adjacent sequences: A076166 A076167 A076168 * A076170 A076171 A076172

KEYWORD

nonn

AUTHOR

Jason Earls, Nov 01 2002

STATUS

approved