Comparison of records in sigma(n)/phi(n) and A018892 ---------------------------------------------------- From Jorg Brown (jorg(AT)google.com), Mar 05 2007 Values of n which represent new highs for A018892 *or* sigma/phi are listed. New max n= 2 A018892= 2, sigma(n)= 3, phi(n)= 1, ratio=3.000000 New max n= 4 A018892= 3, sigma(n)= 7, phi(n)= 2, ratio=3.500000 New max n= 6 A018892= 5, sigma(n)= 12, phi(n)= 2, ratio=6.000000 New max n= 12 A018892= 8, sigma(n)= 28, phi(n)= 4, ratio=7.000000 New max n= 24 A018892= 11, sigma(n)= 60, phi(n)= 8, ratio=7.500000 New max n= 30 A018892= 14, sigma(n)= 72, phi(n)= 8, ratio=9.000000 New max n= 60 A018892= 23, sigma(n)= 168, phi(n)= 16, ratio= 10.500000 New max n= 120 A018892= 32, sigma(n)= 360, phi(n)= 32, ratio= 11.250000 New max n= 180 A018892= 38, sigma(n)= 546, phi(n)= 48, ratio= 11.375000 New max n= 210 A018892= 41, sigma(n)= 576, phi(n)= 48, ratio= 12.000000 New max n= 360 A018892= 53, sigma(n)= 1170, phi(n)= 96, ratio= 12.187500 New max n= 420 A018892= 68, sigma(n)= 1344, phi(n)= 96, ratio= 14.000000 New max n= 840 A018892= 95, sigma(n)= 2880, phi(n)= 192, ratio= 15.000000 New max n= 1260 A018892= 113, sigma(n)= 4368, phi(n)= 288, ratio= 15.166667 New max n= 1680 A018892= 122, sigma(n)= 5952, phi(n)= 384, ratio= 15.500000 New max n= 2520 A018892= 158, sigma(n)= 9360, phi(n)= 576, ratio= 16.250000 New max n= 4620 A018892= 203, sigma(n)= 16128, phi(n)= 960, ratio= 16.800000 New max n= 7560 A018892= 221, sigma(n)= 28800, phi(n)= 1728, ratio= 16.666667 New max n= 9240 A018892= 284, sigma(n)= 34560, phi(n)= 1920, ratio= 18.000000 New max n= 13860 A018892= 338, sigma(n)= 52416, phi(n)= 2880, ratio= 18.200000 New max n= 18480 A018892= 365, sigma(n)= 71424, phi(n)= 3840, ratio= 18.600000 New max n= 27720 A018892= 473, sigma(n)= 112320, phi(n)= 5760, ratio= 19.500000 New max n= 55440 A018892= 608, sigma(n)= 232128, phi(n)= 11520, ratio= 20.150000 New max n= 83160 A018892= 662, sigma(n)= 345600, phi(n)= 17280, ratio= 20.000000 New max n= 110880 A018892= 743, sigma(n)= 471744, phi(n)= 23040, ratio= 20.475000 New max n= 120120 A018892= 851, sigma(n)= 483840, phi(n)= 23040, ratio= 21.000000 New max n= 180180 A018892=1013, sigma(n)= 733824, phi(n)= 34560, ratio= 21.233333 New max n= 240240 A018892=1094, sigma(n)= 999936, phi(n)= 46080, ratio= 21.700000 New max n= 360360 A018892=1418, sigma(n)= 1572480, phi(n)= 69120, ratio= 22.750000 New max n= 720720 A018892=1823, sigma(n)= 3249792, phi(n)= 138240, ratio= 23.508333 New max n=1081080 A018892=1985, sigma(n)= 4838400, phi(n)= 207360, ratio= 23.333333 New max n=1441440 A018892=2228, sigma(n)= 6604416, phi(n)= 276480, ratio= 23.887500 New max n=1801800 A018892=2363, sigma(n)= 8124480, phi(n)= 345600, ratio= 23.508333 New max n=2042040 A018892=2552, sigma(n)= 8709120, phi(n)= 368640, ratio= 23.625000 Non max n=2162160 A018892=2552, sigma(n)= 9999360, phi(n)= 414720, ratio= 24.111111 New max n=2882880 A018892=2633, sigma(n)=13313664, phi(n)= 552960, ratio= 24.077083 New max n=3063060 A018892=3038, sigma(n)=13208832, phi(n)= 552960, ratio= 23.887500 Non max n=3603600 A018892=3038, sigma(n)=16790592, phi(n)= 691200, ratio= 24.291944 New max n=4084080 A018892=3281, sigma(n)=17998848, phi(n)= 737280, ratio= 24.412500 Non max n=4324320 A018892=3119, sigma(n)=20321280, phi(n)= 829440, ratio= 24.500000 New max n=5405400 A018892=3308, sigma(n)=24998400, phi(n)=1036800, ratio= 24.111111 New max n=6126120 A018892=4253, sigma(n)=28304640, phi(n)=1105920, ratio= 25.593750