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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 (list; graph; refs; listen; history; text; internal format)
 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: A374226 A028567 A003359 * A256151 A238471 A259457 Adjacent sequences: A292061 A292062 A292063 * A292065 A292066 A292067 KEYWORD nonn AUTHOR Amiram Eldar, Sep 08 2017 STATUS approved

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Last modified August 13 18:32 EDT 2024. Contains 375144 sequences. (Running on oeis4.)