

A292064


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


0



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
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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

Table of n, a(n) for n=1..39.


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



