Indices of records in A281113. Michael Thomas De Vlieger, St. Louis, Missouri 201710212200. +--------------------------------+ | Indices of records in A281113. | +--------------------------------+ i = table index. k = index of record in A281113. m = record in A281113 = A281113(k). MN(k) = rev(A054841(k)) = multiplicities of primes according to position. Example, 84 = 2^2 * 3 * 7 = "2 1 0 1". i k m MN(k) --------------------------------- 1 2 1 1 2 4 3 2 3 8 6 3 4 12 9 2 1 5 16 15 4 6 24 23 3 1 7 32 28 5 8 36 32 2 2 9 48 58 4 1 10 64 66 6 11 72 84 3 2 12 96 134 5 1 13 144 234 4 2 14 192 309 6 1 15 240 325 4 1 1 16 288 558 5 2 17 384 675 7 1 18 432 721 4 3 19 480 822 5 1 1 20 576 1380 6 2 21 720 1414 4 2 1 22 768 1466 8 1 23 864 1881 5 3 24 960 2011 6 1 1 25 1152 3108 7 2 26 1440 3787 5 2 1 27 1728 4791 6 3 28 2160 5022 4 3 1 29 2304 7137 8 2 30 2880 9741 6 2 1 31 3456 11496 7 3 32 4320 14182 5 3 1 33 4608 15435 9 2 34 5184 15771 6 4 35 5760 23855 7 2 1 36 6912 27071 8 3 37 8640 38097 6 3 1 38 10368 38993 7 4 39 11520 56784 8 2 1 40 13824 61725 9 3 41 17280 97335 7 3 1 42 23040 130912 9 2 1 43 25920 133287 6 4 1 44 27648 137876 10 3 ////// Observations: ////// 1. The powers 2^e with 1 <= e <= 6 appear in k. 2. Numbers in k appear to be products of a contiguous set of the smallest distinct primes. +-------------------------------+ | Primitive terms m in A281113. | +-------------------------------+ For 2 <= n <= A002110(6) = 30030. i = Table index.* k = First position of m in A281113. m = Primitive term in A281113 = A281113(k). MN(k) = rev(A054841(k)) = multiplicities of primes according to position. Example, 84 = 2^2 * 3 * 7 = "2 1 0 1". i* k m MN(k) -------------------------------- 1 2 1 1 2 4 3 2 3 8 6 3 4 12 9 2 1 5 30 12 1 1 1 6 16 15 4 7 24 23 3 1 8 32 28 5 9 36 32 2 2 10 60 41 2 1 1 11 48 58 4 1 12 210 60 1 1 1 1 13 64 66 6 14 72 84 3 2 15 120 119 3 1 1 16 128 122 7 17 96 134 5 1 18 180 155 2 2 1 19 420 231 2 1 1 1 20 144 234 4 2 21 216 254 3 3 22 256 266 8 23 192 309 6 1 24 240 325 4 1 1 25 2310 358 1 1 1 1 1 26 360 485 3 2 1 27 512 503 9 28 288 558 5 2 29 900 653 2 2 2 30 384 675 7 1 31 432 721 4 3 32 840 745 3 1 1 1 33 480 822 5 1 1 34 1260 972 2 2 1 1 35 1024 1027 10 36 576 1380 6 2 37 720 1414 4 2 1 38 768 1466 8 1 39 4620 1534 2 1 1 1 1 40 1080 1633 3 3 1 41 864 1881 5 3 42 2048 1913 11 43 960 2011 6 1 1 44 1800 2156 3 2 2 45 1680 2197 4 1 1 1 46 1296 2208 4 4 47 30030 2471 1 1 1 1 1 1 48 1536 3085 9 1 49 1152 3108 7 2 50 2520 3367 3 2 1 1 51 1440 3787 5 2 1 52 4096 3874 12 53 6300 4439 2 2 2 1 54 1920 4704 7 1 1 55 1728 4791 6 3 56 2160 5022 4 3 1 57 9240 5418 3 1 1 1 1 58 2592 5912 5 4 59 3360 5986 5 1 1 1 60 3072 6432 10 1 61 3600 6741 4 2 2 62 8192 7099 13 63 13860 7121 2 2 1 1 1 64 2304 7137 8 2 65 5400 7764 3 3 2 66 2880 9741 6 2 1 67 5040 10546 4 2 1 1 68 3840 10739 8 1 1 69 3456 11496 7 3 70 7560 12429 3 3 1 1 71 6144 13101 11 1 72 16384 13799 14 73 4320 14182 5 3 1 74 4608 15435 9 2 75 6720 15527 6 1 1 1 76 5184 15771 6 4 77 6480 16207 4 4 1 78 12600 16439 3 2 2 1 79 7776 16882 5 5 80 18480 17157 4 1 1 1 1 81 7200 18887 5 2 2 82 7680 23831 9 1 1 83 5760 23855 7 2 1 84 10800 25332 4 3 2 85 12288 26550 12 1 86 27720 26876 3 2 1 1 1 87 6912 27071 8 3 88 27000 29863 3 3 3 89 10080 30323 5 2 1 1 90 9216 33671 10 2 91 8640 38097 6 3 1 92 13440 38461 7 1 1 1 93 10368 38993 7 4 94 15120 40989 4 3 1 1 95 15552 46239 6 5 96 12960 47751 5 4 1 97 14400 51209 6 2 2 98 15360 51880 10 1 1 99 24576 52803 13 1 100 25200 54520 4 2 2 1 101 11520 56784 8 2 1 102 13824 61725 9 3 103 18432 70456 11 2 104 21600 75342 5 3 2 105 20160 82463 6 2 1 1 106 26880 92160 8 1 1 1 107 20736 95613 8 4 108 17280 97335 7 3 1 109 28800 130348 7 2 2 110 23040 130912 9 2 1 111 25920 133287 6 4 1 112 27648 137876 10 3 * Note: the index pertains only to the range indicated. Other terms m may interpose between the ones listed here. ////// Observations: ////// 1. All terms k are even. 2. The powers of 2 appear to be in the sequence k. 3. The primorials A002110(j) for 1 <= j <= 6 appear in k. (eof)