A287473 -id:A287473 - cp's OEIS frontend

A292064 Triangular numbers k such that psi(k) is a square, where psi(k) is the Dedekind psi function (A001615).

1, 3, 66, 210, 276, 1128, 2346, 2556, 4278, 5778, 7140, 7750, 7875, 11781, 13041, 18336, 22578, 27966, 28920, 31878, 32131, 32640, 35511, 51681, 70125, 73536, 79800, 89676, 93096, 100128, 102378, 122760, 139128, 169653, 173755, 177906, 209628, 223446, 253116

Offset: 1

Amiram Eldar, Sep 08 2017

nonn

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, ...
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, ...
Intersection of A000217 and A291167. - Altug Alkan, Sep 08 2017

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

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

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

psi[n_] := If[n<1, 0, n*Sum[MoebiusMu[d]^2/d, {d, Divisors @ n}]];
Select[Accumulate[Range[1000]], IntegerQ[Sqrt[psi[#]]]&]

cp's OEIS Frontend

A292064 Triangular numbers k such that psi(k) is a square, where psi(k) is the Dedekind psi function (A001615).

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