Search a number
deficient n.  and  Hogben n.

First numbers that belong to both sets:

1, 3, 7, 13, 21, 31, 43, 57, 73, 91, 111, 133, 157, 183, 211, 241, 273, 307, 343, 381, 421, 463, 507, 553, 601, 651, 703, 757, 813, 871, 931, 993, 1057, 1123, 1191, 1261, 1333, 1407, 1483, 1561, 1641, 1723, 1807, 1893, 1981, 2071, 2163, 2257, 2353, 2451, 2551, 2653, 2757, 2863, 2971, 3081, 3193, 3307, 3423, 3541, 3661, 3783, 3907, 4033, 4161, 4291, 4423, 4557, 4693, 4831, 4971, 5113, 5257, 5403, 5551, 5701, 5853, 6007, 6163, 6321, 6481, 6643, 6807, 6973, 7141, 7311, 7483, 7657, 7833, 8011, 8191, 8373, 8557, 8743, 8931, 9121, 9313, 9507, 9703, 9901, 10101, 10303, 10507, 10713, 10921, 11131, 11343, 11557, 11773, 11991, 12211, 12433, 12657, 12883, 13111, 13341, 13573, 13807, 14043, 14281, 14521, 14763, 15007, 15253, 15501, 15751, 16003, 16257, 16513, 16771, 17031, 17293, 17557, 17823, 18091, 18361, 18633, 18907, 19183, 19461, 19741, 20023, 20307, 20593, 20881, 21171, 21463, 21757, 22053, 22351, 22651, 22953, 23257, 23563, 23871, 24181, 24493, 24807, 25123, 25441, 25761, 26083, 26407, 26733, 27061, 27391, 27723, 28057, 28393, 28731, 29071, 29413, 29757, 30103, 30451, 30801, 31153, 31507, 31863, 32221, 32581, 32943, 33307, 33673, 34041, 34411, 34783, 35157, 35533, 35911, 36291, 36673, 37057, 37443, 37831, 38221, 38613, 39007, 39403, 39801, 40201, 40603, 41007, 41413, 41821, 42231, 42643, 43057, 43473, 43891, 44311, 44733, 45157, 45583, 46011, 46441, 46873, 47307, 47743, 48181, 48621, 49063, 49507, 49953, 50401, 50851, 51303, 51757, 52213, 52671, 53131, 53593, 54057, 54523, 54991, 55461, 55933, 56407, 56883, 57361, 57841, 58323, 58807, 59293, 59781, 60271, 60763, 61257, 61753, 62251, 62751, 63253, 63757, 64263, 64771, 65281, 65793, 66307, 66823, 67341, 67861, 68383, 68907, 69433, 69961, 70491, 71023, 71557, 72093, 72631, 73171, 73713, 74257, 74803, 75351, 75901, 76453, 77007, 77563, 78121.

Some larger examples :