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%I #9 Sep 11 2017 05:47:48
%S 1,780,2775,5050,474825,681528,1727011,5286126,5911641,6604795,
%T 17325441,21612025,27799696,45025305,386767578,1538599128,2086160121,
%U 3679490220,5718242211,7092226351,8019794628,16505718895,36604197735,55541611986,56693041356,89369984476
%N Triangular numbers n such that psi(n) is also a triangular number, where psi is the Dedekind psi function (A001615).
%C The indices of these triangular numbers are 1, 39, 74, 100, 974, 1167, 1858, 3251, 3438, 3634, 5886, 6574, 7456, 9489, ...
%C The indices of the triangular psi values are 1, 63, 95, 135, 1280, 1664, 2015, 4607, 4095, 4095, 7424, 7424, 9152, 12543, ...
%H Giovanni Resta, <a href="/A292063/b292063.txt">Table of n, a(n) for n = 1..100</a>
%e 780 is in the sequence since 780 = 39*40/2 is triangular and psi(780) = 2016 = 63*64/2 is also triangular.
%t psi[n_] := If[n<1, 0, n*Sum[MoebiusMu[d]^2/d, {d, Divisors @ n}]]; triQ[n_] := IntegerQ@ Sqrt[8n+1]; Select[Accumulate[Range[1000]], triQ[psi[#]]&]
%Y Cf. A000217, A001615, A083674, A083675, A115910, A116541, A287472.
%K nonn
%O 1,2
%A _Amiram Eldar_, Sep 08 2017
%E a(18)-a(26) from _Giovanni Resta_, Sep 11 2017