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A391289

Integers x such that there exist three integers 0<x<=y<=z and t>0 such that psi(x)^2 = psi(y)^2 = psi(z)^2 = x^2 + y^2 + z^2 + t^2.

6, 12, 18, 24, 36, 48, 54, 72, 96, 108, 144, 162, 192, 216, 288, 324, 384, 432, 486, 576, 648, 768, 864, 972, 1152, 1296, 1450, 1458, 1536, 1728, 1944, 2304, 2592, 2900, 2916, 3072, 3456, 3888, 4374, 4608, 5184, 5800, 5832, 6144, 6912, 7250, 7776, 8748, 9216, 10368, 11600, 11664, 12288, 13122, 13824

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OFFSET

1,1

COMMENTS

The numbers x, y, z and t form a psi-quadratic quadruple.

LINKS

Table of n, a(n) for n=1..55.

S. I. Dimitrov, On psi-quadratic k-tuples and their generalizations, arXiv:2509.18291 [math.NT], 2025.

EXAMPLE

(36, 44, 44, 4) is such a quadruple because psi(36)^2 = psi(44)^2 = psi(44)^2 = 72^2 = 36^2 + 44^2 + 44^2 + 4^2.

CROSSREFS

Cf. A000414, A001615, A385531.