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congruent n.  and  Eulerian n.

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First numbers that belong to both sets:

120, 247, 302, 502, 1013, 1191, 2036, 2416, 4293, 32752, 47840, 65519, 131054, 152637, 156190, 262125, 455192, 478271, 1479726, 2097130, 2203488.