A292063 Triangular numbers n such that psi(n) is also a triangular number, where psi is the Dedekind psi function (A001615).

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

Offset

1,2

Comments

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, ...

Links

Giovanni Resta, Table of n, a(n) for n = 1..100

Example

780 is in the sequence since 780 = 39*40/2 is triangular and psi(780) = 2016 = 63*64/2 is also triangular.

Mathematica

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[#]]&]

Crossrefs

Cf. A000217, A001615, A083674, A083675, A115910, A116541, A287472.

Sequence in context: A147547 A259924 A135198 * A250952 A139400 A115467

Adjacent sequences: A292060 A292061 A292062 * A292064 A292065 A292066

Keyword

nonn

Author

Amiram Eldar, Sep 08 2017

Extensions

a(18)-a(26) from Giovanni Resta, Sep 11 2017

Status

approved