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A292063
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Triangular numbers n such that psi(n) is also a triangular number, where psi is the Dedekind psi function (A001615).
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1
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1, 780, 2775, 5050, 474825, 681528, 1727011, 5286126, 5911641, 6604795, 17325441, 21612025, 27799696, 45025305, 386767578, 1538599128, 2086160121, 3679490220, 5718242211, 7092226351, 8019794628, 16505718895, 36604197735, 55541611986, 56693041356, 89369984476
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OFFSET
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1,2
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COMMENTS
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The indices of these triangular numbers are 1, 39, 74, 100, 974, 1167, 1858, 3251, 3438, 3634, 5886, 6574, 7456, 9489, ...
The indices of the triangular psi values are 1, 63, 95, 135, 1280, 1664, 2015, 4607, 4095, 4095, 7424, 7424, 9152, 12543, ...
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LINKS
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EXAMPLE
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780 is in the sequence since 780 = 39*40/2 is triangular and psi(780) = 2016 = 63*64/2 is also triangular.
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MATHEMATICA
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psi[n_] := If[n<1, 0, n*Sum[MoebiusMu[d]^2/d, {d, Divisors @ n}]]; triQ[n_] := IntegerQ@ Sqrt[8n+1]; Select[Accumulate[Range[1000]], triQ[psi[#]]&]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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