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A292064
Triangular numbers k such that psi(k) is a square, where psi(k) is the Dedekind psi function (A001615).
1
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 08 2017
STATUS
approved