A292064 - OEIS

%I #17 Apr 06 2023 08:30:24

%S 1,3,66,210,276,1128,2346,2556,4278,5778,7140,7750,7875,11781,13041,

%T 18336,22578,27966,28920,31878,32131,32640,35511,51681,70125,73536,

%U 79800,89676,93096,100128,102378,122760,139128,169653,173755,177906,209628,223446,253116

%N Triangular numbers k such that psi(k) is a square, where psi(k) is the Dedekind psi function (A001615).

%C The indices of these triangular numbers are 1, 2, 11, 20, 23, 47, 68, 71, 92, 107, 119, 124, 125, 153, 161, 191, 212, 236, 240, ...

%C The indices of the square psi values are 1, 2, 12, 24, 24, 48, 72, 72, 96, 108, 144, 120, 120, 144, 144, 192, 216, 240, 264, ...

%C Intersection of A000217 and A291167. - _Altug Alkan_, Sep 08 2017

%H Amiram Eldar, <a href="/A292064/b292064.txt">Table of n, a(n) for n = 1..10000</a>

%e 66 is in the sequence since 66 = 11*12/2 is triangular, and psi(66) = 144 = 12^2 is square.

%t psi[n_] := If[n<1, 0, n*Sum[MoebiusMu[d]^2/d, {d, Divisors @ n}]];

%t Select[Accumulate[Range[1000]], IntegerQ[Sqrt[psi[#]]]&]

%Y Cf. A000217, A000290, A001615, A287473, A291167.

%K nonn

%O 1,2

%A _Amiram Eldar_, Sep 08 2017