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practical numbers
A number n such that all the smaller numbers can be written as the sum of distinct proper divisors of n. more

The first 600 practical numbers :
1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66, 72, 78, 80, 84, 88, 90, 96, 100, 104, 108, 112, 120, 126, 128, 132, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 240, 252, 256, 260, 264, 270, 272, 276, 280, 288, 294, 300, 304, 306, 308, 312, 320, 324, 330, 336, 340, 342, 348, 352, 360, 364, 368, 378, 380, 384, 390, 392, 396, 400, 408, 414, 416, 420, 432, 440, 448, 450, 456, 460, 462, 464, 468, 476, 480, 486, 496, 500, 504, 510, 512, 520, 522, 528, 532, 540, 544, 546, 552, 558, 560, 570, 576, 580, 588, 594, 600, 608, 612, 616, 620, 624, 630, 640, 644, 648, 660, 666, 672, 680, 684, 690, 696, 700, 702, 704, 714, 720, 726, 728, 736, 740, 744, 750, 756, 760, 768, 780, 784, 792, 798, 800, 810, 812, 816, 820, 828, 832, 840, 858, 860, 864, 868, 870, 880, 882, 888, 896, 900, 912, 918, 920, 924, 928, 930, 936, 952, 960, 966, 968, 972, 980, 984, 990, 992, 1000, 1008, 1014, 1020, 1024, 1026, 1032, 1036, 1040, 1044, 1050, 1056, 1064, 1080, 1088, 1092, 1100, 1104, 1110, 1116, 1120, 1122, 1128, 1134, 1140, 1144, 1148, 1152, 1160, 1170, 1176, 1184, 1188, 1200, 1204, 1216, 1218, 1224, 1230, 1232, 1240, 1242, 1248, 1254, 1260, 1272, 1280, 1288, 1290, 1296, 1300, 1302, 1312, 1316, 1320, 1326, 1332, 1344, 1350, 1352, 1360, 1368, 1372, 1376, 1380, 1386, 1392, 1400, 1404, 1408, 1410, 1416, 1428, 1440, 1452, 1456, 1458, 1464, 1470, 1472, 1476, 1480, 1482, 1484, 1488, 1496, 1500, 1504, 1512, 1518, 1520, 1530, 1536, 1540, 1548, 1554, 1560, 1566, 1568, 1584, 1590, 1596, 1600, 1620, 1624, 1632, 1638, 1640, 1650, 1656, 1664, 1672, 1674, 1680, 1692, 1696, 1700, 1710, 1716, 1720, 1722, 1728, 1736, 1740, 1760, 1764, 1768, 1770, 1776, 1782, 1792, 1794, 1800, 1806, 1820, 1824, 1830, 1836, 1840, 1848, 1856, 1860, 1872, 1880, 1888, 1890, 1900, 1904, 1908, 1914, 1920, 1932, 1936, 1944, 1950, 1952, 1960, 1968, 1974, 1976, 1980, 1984, 1998, 2000, 2010, 2016, 2024, 2028, 2040, 2046, 2048, 2052, 2058, 2064, 2070, 2072, 2080, 2088, 2100, 2106, 2112, 2120, 2124, 2128, 2130, 2142, 2156, 2160, 2176, 2178, 2184, 2190, 2196, 2200, 2208, 2214, 2220, 2226, 2232, 2240, 2244, 2250, 2256, 2262, 2268, 2280, 2288, 2296, 2300, 2304, 2310, 2320, 2322, 2340, 2352, 2360, 2368, 2376, 2380, 2392, 2394, 2400, 2408, 2412, 2418, 2420, 2430, 2432, 2436, 2440, 2442, 2448, 2460, 2464, 2478, 2480, 2484, 2496, 2500, 2508, 2520, 2538, 2544, 2548, 2550, 2552, 2556, 2560, 2562, 2574, 2576, 2580, 2592, 2600, 2604, 2610, 2624, 2628, 2632, 2640, 2646, 2652, 2660, 2664, 2680, 2688, 2700, 2704, 2706, 2720, 2728, 2730, 2736, 2744, 2752, 2754, 2760, 2772, 2784, 2790, 2800, 2808, 2814, 2816, 2820, 2832, 2838, 2840, 2844, 2850, 2856, 2860, 2862, 2880, 2886, 2898, 2900, 2904, 2912, 2916, 2920, 2928, 2940, 2944, 2952, 2960, 2964, 2968, 2970, 2976, 2982, 2988, 2992, 3000, 3008, 3016, 3024, 3036, 3040, 3042, 3060, 3066, 3072, 3078, 3080, 3096, 3100, 3102, 3108, 3120, 3132, 3136, 3150, 3160, 3168, 3180, 3186, 3192, 3198, 3200, 3204, 3216, 3220, 3224, 3234, 3240, 3248, 3256, 3264, 3276, 3280, 3294, 3300, 3304, 3312, 3318, 3320, 3328, 3330, 3332, 3344, 3348, 3354, 3360, 3366, 3380, 3384, 3388, 3392, 3400, 3402, 3408, 3416, 3420, 3432, 3440, 3444, 3450, 3456, 3468, 3472, 3480, 3486, 3498, 3500, 3504, 3510, 3520, 3528, 3536, 3540, 3552, 3560, 3564, 3570, 3584, 3588, 3600, 3608, 3612, 3618, 3630, 3640.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 829157 values, from 1 to 10000000).

n\r 0  1 
28291561 2 
3535172146985147000 3 
464187511872810 4 
5309866129847129819129810129815 5 
6535172114700001469840 6 
7239022983749834898318983529840898335 7 
843232819363502095470936460 8 
9256842489704896013913548985490261391954903049014 9 
1030986611298190129815012984601298100 10 
1115552267360673916732367365673516729467448674046736167338

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.