A number which is the product of 3 distinct primes. more
The first 600 sphenic numbers :
30,
42,
66,
70,
78,
102,
105,
110,
114,
130,
138,
154,
165,
170,
174,
182,
186,
190,
195,
222,
230,
231,
238,
246,
255,
258,
266,
273,
282,
285,
286,
290,
310,
318,
322,
345,
354,
357,
366,
370,
374,
385,
399,
402,
406,
410,
418,
426,
429,
430,
434,
435,
438,
442,
455,
465,
470,
474,
483,
494,
498,
506,
518,
530,
534,
555,
561,
574,
582,
590,
595,
598,
602,
606,
609,
610,
615,
618,
627,
638,
642,
645,
646,
651,
654,
658,
663,
665,
670,
678,
682,
705,
710,
715,
730,
741,
742,
754,
759,
762,
777,
782,
786,
790,
795,
805,
806,
814,
822,
826,
830,
834,
854,
861,
874,
885,
890,
894,
897,
902,
903,
906,
915,
935,
938,
942,
946,
957,
962,
969,
970,
978,
986,
987,
994,
1001,
1002,
1005,
1010,
1015,
1022,
1023,
1030,
1034,
1038,
1045,
1054,
1065,
1066,
1070,
1074,
1085,
1086,
1090,
1095,
1102,
1105,
1106,
1113,
1118,
1130,
1131,
1146,
1158,
1162,
1166,
1173,
1178,
1182,
1185,
1194,
1209,
1221,
1222,
1235,
1239,
1245,
1246,
1258,
1265,
1266,
1270,
1281,
1295,
1298,
1309,
1310,
1311,
1334,
1335,
1338,
1342,
1353,
1358,
1362,
1370,
1374,
1378,
1390,
1394,
1398,
1406,
1407,
1414,
1419,
1426,
1434,
1435,
1442,
1443,
1446,
1455,
1462,
1463,
1474,
1479,
1490,
1491,
1495,
1498,
1505,
1506,
1510,
1515,
1526,
1533,
1534,
1542,
1545,
1547,
1551,
1558,
1562,
1570,
1578,
1581,
1582,
1586,
1595,
1598,
1599,
1605,
1606,
1614,
1615,
1626,
1630,
1634,
1635,
1645,
1653,
1659,
1662,
1670,
1677,
1686,
1695,
1698,
1702,
1705,
1729,
1730,
1738,
1742,
1743,
1749,
1758,
1767,
1771,
1778,
1786,
1790,
1798,
1802,
1810,
1826,
1833,
1834,
1842,
1846,
1855,
1866,
1869,
1878,
1885,
1886,
1887,
1898,
1902,
1905,
1910,
1918,
1930,
1946,
1947,
1955,
1958,
1965,
1970,
1978,
1986,
1990,
2001,
2006,
2013,
2014,
2015,
2022,
2035,
2037,
2054,
2055,
2065,
2067,
2074,
2082,
2085,
2086,
2091,
2093,
2094,
2109,
2110,
2114,
2118,
2121,
2134,
2135,
2139,
2146,
2154,
2158,
2162,
2163,
2185,
2193,
2198,
2202,
2211,
2222,
2230,
2233,
2235,
2238,
2242,
2247,
2255,
2261,
2265,
2266,
2270,
2274,
2278,
2282,
2289,
2290,
2294,
2298,
2301,
2314,
2318,
2330,
2334,
2337,
2338,
2343,
2345,
2354,
2355,
2365,
2373,
2378,
2379,
2382,
2387,
2390,
2397,
2398,
2405,
2406,
2409,
2410,
2414,
2422,
2431,
2438,
2445,
2451,
2454,
2465,
2482,
2485,
2486,
2494,
2505,
2506,
2510,
2514,
2522,
2526,
2534,
2542,
2546,
2553,
2555,
2570,
2585,
2586,
2595,
2598,
2607,
2613,
2626,
2630,
2634,
2635,
2639,
2658,
2665,
2666,
2667,
2674,
2678,
2679,
2685,
2686,
2690,
2694,
2697,
2698,
2702,
2703,
2710,
2714,
2715,
2717,
2726,
2737,
2739,
2742,
2751,
2755,
2758,
2765,
2766,
2769,
2770,
2774,
2778,
2782,
2786,
2794,
2795,
2802,
2806,
2810,
2821,
2822,
2829,
2830,
2834,
2847,
2849,
2865,
2874,
2877,
2882,
2895,
2905,
2914,
2915,
2919,
2922,
2930,
2937,
2938,
2945,
2946,
2954,
2955,
2967,
2985,
2994,
3002,
3009,
3014,
3018,
3021,
3026,
3034,
3054,
3055,
3058,
3059,
3070,
3074,
3081,
3082,
3110,
3111,
3115,
3122,
3126,
3129,
3130,
3138,
3145,
3154,
3157,
3165,
3170,
3171,
3178,
3182,
3201,
3206,
3219,
3237,
3243,
3245,
3246,
3262,
3266,
3278,
3282,
3286,
3289,
3297,
3298,
3302,
3310,
3311,
3322,
3333,
3335,
3342,
3345,
3346,
3355,
3358,
3363,
3367,
3370,
3374,
3378,
3382,
3395,
3399,
3405,
3406,
3414,
3417,
3422,
3423,
3426,
3434,
3435,
3441,
3445,
3451,
3454,
3462,
3470,
3471,
3477,
3478,
3485,
3490,
3495,
3502,
3507,
3514,
3515,
3522,
3526,
3530,
3531,
3535,
3538,
3553,
3558,
3562,
3565,
3567,
3585,
3586,
3590,
3594,
3597,
3598,
3605,
3606,
3614,
3615,
3619,
3621,
3633,
3634,
3638,
3642.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 20710806 values, from 30 to 99999994).
n\r | 0 | 1 |
2 | 7373736 | 13337070 | 2 |
3 | 5318673 | 7696864 | 7695269 | 3 |
4 | 0 | 6669127 | 7373736 | 6667943 | 4 |
5 | 3420588 | 4322539 | 4321958 | 4323061 | 4322660 | 5 |
6 | 1071203 | 4545229 | 3150898 | 4247470 | 3151635 | 4544371 | 6 |
7 | 2529290 | 3029816 | 3030595 | 3029595 | 3030445 | 3030070 | 3030995 | 7 |
8 | 0 | 3334927 | 3686635 | 3334070 | 0 | 3334200 | 3687101 | 3333873 | 8 |
9 | 0 | 2565467 | 2565289 | 2659697 | 2566166 | 2564793 | 2658976 | 2565231 | 2565187 | 9 |
10 | 664577 | 2645322 | 1676839 | 2645295 | 1677337 | 2756011 | 1677217 | 2645119 | 1677766 | 2645323 | 10 |
11 | 1671265 | 1904069 | 1904435 | 1903504 | 1903022 | 1904399 | 1903225 | 1905198 | 1903729 | 1903784 | 1904176 |
A pictorial representation of the table above
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.