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Number of integer partitions of n where the parts do not have the same median as the distinct parts.
+10
18
0, 0, 0, 0, 1, 3, 3, 9, 11, 17, 23, 37, 42, 68, 87, 110, 153, 209, 261, 352, 444, 573, 750, 949, 1187, 1508, 1909, 2367, 2938, 3662, 4507, 5576, 6826, 8359, 10203, 12372, 15011, 18230, 21996, 26518, 31779, 38219, 45682, 54660, 65112, 77500, 92089, 109285
Number of integer partitions of n where the parts have the same median as the distinct parts.
+10
17
1, 1, 2, 3, 4, 4, 8, 6, 11, 13, 19, 19, 35, 33, 48, 66, 78, 88, 124, 138, 183, 219, 252, 306, 388, 450, 527, 643, 780, 903, 1097, 1266, 1523, 1784, 2107, 2511, 2966, 3407, 4019, 4667, 5559, 6364, 7492, 8601, 10063, 11634, 13469, 15469, 17985, 20558, 23812
Number of integer partitions of n whose distinct parts have integer mean.
+10
16
0, 1, 2, 2, 4, 3, 8, 6, 13, 13, 22, 19, 43, 34, 56, 66, 97, 92, 156, 143, 233, 256, 322, 341, 555, 542, 710, 831, 1098, 1131, 1644, 1660, 2275, 2484, 3035, 3492, 4731, 4848, 6063, 6893, 8943, 9378, 12222, 13025, 16520, 18748, 22048, 24405, 31446, 33698, 41558
Number of integer partitions of n where the parts do not have the same mean as the distinct parts.
+10
14
0, 0, 0, 0, 1, 3, 3, 9, 11, 19, 25, 43, 49, 82, 103, 136, 183, 258, 314, 435, 524, 687, 892, 1150, 1378, 1788, 2241, 2773, 3399, 4308, 5142, 6501, 7834, 9600, 11726, 14099, 16949, 20876, 25042, 30032, 35732, 43322, 51037, 61650, 72807, 86319, 102983, 122163
Number of integer partitions of n where the parts have the same mean as the distinct parts.
+10
14
1, 1, 2, 3, 4, 4, 8, 6, 11, 11, 17, 13, 28, 19, 32, 40, 48, 39, 71, 55, 103, 105, 110, 105, 197, 170, 195, 237, 319, 257, 462, 341, 515, 543, 584, 784, 1028, 761, 973, 1153, 1606, 1261, 2137, 1611, 2368, 2815, 2575, 2591, 4393, 3798, 4602, 4663, 5777, 5121
Numbers for which the prime indices do not have the same mean as the distinct prime indices.
+10
12
12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 68, 72, 75, 76, 80, 84, 88, 92, 96, 98, 99, 104, 108, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 144, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189
Numbers for which the prime indices have the same mean as the distinct prime indices.
+10
12
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 100, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119, 121, 122, 123, 125, 127, 128, 129, 130
Number of integer partitions of n where the parts have lesser mean than the distinct parts.
+10
10
0, 0, 0, 0, 1, 2, 3, 7, 9, 16, 22, 34, 44, 69, 88, 118, 163, 221, 280, 376, 473, 619, 800, 1016, 1257, 1621, 2038, 2522, 3117, 3921, 4767, 5964, 7273, 8886, 10838, 13141, 15907, 19468, 23424, 28093, 33656, 40672, 48273, 58171, 68944, 81888, 97596, 115643
Numbers for which the prime indices have greater mean than the distinct prime indices.
+10
9
18, 50, 54, 75, 98, 108, 147, 150, 162, 242, 245, 250, 294, 324, 338, 350, 363, 375, 450, 486, 490, 500, 507, 578, 588, 605, 648, 686, 722, 726, 735, 750, 845, 847, 867, 882, 972, 1014, 1029, 1050, 1058, 1078, 1083, 1125, 1183, 1210, 1250, 1274, 1350, 1372
Numbers for which the prime indices have lesser mean than the distinct prime indices.
+10
9
12, 20, 24, 28, 40, 44, 45, 48, 52, 56, 60, 63, 68, 72, 76, 80, 84, 88, 92, 96, 99, 104, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 144, 148, 152, 153, 156, 160, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189, 192, 198, 200, 204, 207, 208, 212, 220
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