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

1,2

Comments

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

Links

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A091470 A028567 A003359 * A256151 A238471 A259457

Adjacent sequences: A292061 A292062 A292063 * A292065 A292066 A292067

Keyword

nonn

Author

Amiram Eldar, Sep 08 2017

Status

approved