experimental-projects/oeis-research/Michel Marcus/Smallest m such that gcd of the x's that satisfy sigma(x) = m is n/sort_upperbounds.sf

#!/usr/bin/ruby

var easy = Set(1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 18, 19, 22, 27, 29, 32, 36, 37, 43, 45, 49, 50, 61, 64, 67, 72, 73, 81, 91, 98, 100, 101, 106, 109, 121, 128, 129, 133, 134, 137, 146, 148, 149, 152, 157, 162, 163, 169, 171, 173, 192, 193, 197, 199, 200, 202, 211, 217, 218, 219, 229, 241, 243, 256, 257, 259, 262, 268, 274, 277, 281, 283, 288, 289, 292, 301, 313, 314, 317, 324, 331, 333, 337, 338, 343, 347, 349, 353, 361, 367, 373, 379, 381, 386, 388, 392, 397, 400, 401, 404, 409, 411, 421, 422, 427, 441, 448, 450, 457, 458, 461, 463, 469, 484, 487, 489, 499, 505, 507, 509, 511, 512, 519, 523, 529, 541, 544, 547, 548, 549, 554, 556, 559, 562, 563, 566, 576, 577, 578, 579, 601, 613, 617, 625, 628, 633, 641, 643, 648, 652, 653, 657, 661, 662, 673, 676, 677, 691, 703, 709, 721, 722, 729, 733, 739, 746, 751, 757, 768, 772, 776, 787, 800, 802, 811, 821, 823, 829, 831, 841, 842, 843, 849, 853, 857, 859, 867, 871, 872, 876, 877, 882, 900, 907, 909, 937, 939, 949, 961, 968, 977, 982, 997, 1009, 1021, 1024, 1033, 1042, 1051, 1058, 1059, 1069, 1082, 1089, 1093, 1094, 1099, 1108, 1117, 1119, 1123, 1129, 1141, 1145, 1152, 1153, 1156, 1164, 1171, 1172, 1181, 1186, 1191, 1192, 1200, 1201, 1213, 1227, 1228, 1233, 1234, 1237, 1249, 1250, 1252, 1256, 1261, 1263, 1268, 1273, 1277, 1282, 1283, 1285, 1289, 1291, 1297, 1303, 1306, 1307, 1314, 1321, 1322, 1324, 1346, 1351, 1352, 1354, 1359, 1361, 1368, 1369, 1381, 1382, 1387, 1389, 1396, 1409, 1415, 1417, 1423, 1433, 1444, 1447, 1453, 1458, 1459, 1466, 1477, 1489, 1493, 1521, 1531, 1539, 1543, 1546, 1549, 1553, 1557, 1565, 1568, 1569, 1574, 1579, 1588, 1591, 1597, 1600, 1601, 1603, 1613, 1618, 1621, 1623, 1627, 1636, 1641, 1642, 1655, 1657, 1658, 1669, 1681, 1682, 1687, 1688, 1696, 1697, 1699, 1706, 1721, 1723, 1728, 1741, 1747, 1753, 1765, 1783, 1787, 1789, 1791, 1800, 1801, 1803, 1811, 1813, 1814, 1818, 1821, 1828, 1844, 1849, 1856, 1867, 1873, 1875, 1877, 1879, 1882, 1893, 1899, 1901, 1913, 1922, 1923, 1933, 1939, 1954, 1959, 1964, 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64346, 64352, 64373, 64378, 64381, 64406, 64409, 64417, 64424, 64433, 64443, 64451, 64466, 64474, 64479, 64483, 64485, 64489, 64502, 64513, 64516, 64529, 64551, 64552, 64564, 64569, 64576, 64577, 64579, 64585, 64587, 64591, 64593, 64601, 64613, 64618, 64621, 64627, 64633, 64639, 64642, 64646, 64663, 64667, 64671, 64682, 64687, 64705, 64706, 64711, 64717, 64737, 64742, 64747, 64754, 64767, 64783, 64793, 64800, 64802, 64807, 64808, 64811, 64817, 64822, 64827, 64831, 64835, 64839, 64849, 64858, 64861, 64877, 64882, 64886, 64891, 64901, 64909, 64917, 64934, 64936, 64937, 64939, 64951, 64962, 64969, 64971, 64982, 64983, 64984, 64994, 64997, 65003, 65011, 65015, 65019, 65029, 65033, 65034, 65041, 65053, 65061, 65062, 65063, 65066, 65068, 65089, 65092, 65101, 65103, 65111, 65115, 65122, 65138, 65143, 65146, 65147, 65167, 65173, 65174, 65179, 65185, 65187, 65200, 65203, 65209, 65234, 65242, 65253, 65257, 65269, 65271, 65287, 65293, 65309, 65315, 65316, 65319, 65323, 65332, 65336, 65353, 65357, 65359, 65371, 65381, 65385, 65401, 65402, 65413, 65419, 65426, 65432, 65437, 65451, 65461, 65463, 65465, 65476, 65497, 65498, 65521, 65522, 65523, 65533, 65536, 65537, 65539, 65542, 65543, 65551, 65557, 65558, 65563, 65572, 65574, 65587, 65594, 65613, 65617, 65629, 65633, 65651, 65657, 65666, 65668, 65672, 65677, 65707, 65713, 65717, 65719, 65729, 65731, 65732, 65738, 65761, 65768, 65781, 65797, 65809, 65812, 65821, 65829, 65833, 65834, 65837, 65839, 65851, 65864, 65867, 65881, 65882, 65883, 65885, 65899, 65908, 65911, 65921, 65924, 65929, 65942, 65947, 65954, 65957, 65971, 65972, 65973, 65981, 65983, 65997, 66001, 66009, 66031, 66039, 66043, 66049, 66050, 66067, 66071, 66073, 66074, 66081, 66085, 66089, 66097, 66103, 66106, 66109, 66114, 66137, 66139, 66146, 66152, 66153, 66161, 66169, 66173, 66179, 66181, 66182, 66186, 66193, 66199, 66211, 66226, 66245, 66248, 66250, 66268, 66279, 66292, 66301, 66313, 66322, 66333, 66337, 66339, 66343, 66344, 66346, 66349, 66361, 66362, 66369, 66373, 66376, 66377, 66387, 66391, 66412, 66413, 66438)
var table = Hash()

ARGF.each{|line|

    if (line =~ /^a\((\d+)\) <= (\d+)/) { |m|
        var n = m[0]
        var k = m[1].to_i

        if (!table.has(n)) {
            table{n} = k
        }

        if (k < table{n}) {
            table{n} = k
        }
    }
}

for n in (table.keys.map{.to_i}.sort) {

    next if (easy.has(n))
    next if (n > table{n})      # ignore trivial solutions

    say "a(#{n}) <= #{table{n}}"
}