A127668: Indices of primes in prime number decomposition of n>=2 [1, 2, 11, 3, 21, 4, 111, 22, 31, 5, 211, 6, 41, 32, 1111, 7, 221, 8, 311, 42, 51, 9, 2111, 33, 61, 222, 411, 10, 321, 11, 11111, 52, 71, 43, 2211, 12, 81, 62, 3111, 13, 421, 14, 511, 322, 91, 15, 21111, 44, 331, 72, 611, 16, 2221, 53, 4111, 82, 101, 17, 3211, 18, 111, 422, 111111, 63, 521, 19, 711, 92, 431, 20, 22111, 21, 121, 332, 811, 54, 621, 22, 31111, 2222, 131, 23, 4211, 73, 141, 102, 5111, 24, 3221, 64, 911, 112, 151, 83, 211111, 25, 441, 522, 3311] Not a unique representation; not an invertible mapping N\{1} -> N. ############################################################################### Unique representation if lists are used: n a(n) as a list 2 [1] 3 [2] 4 [1, 1] 5 [3] 6 [2, 1] 7 [4] 8 [1, 1, 1] 9 [2, 2] 10 [3, 1] 11 [5] 12 [2, 1, 1] 13 [6] 14 [4, 1] 15 [3, 2] 16 [1, 1, 1, 1] 17 [7] 18 [2, 2, 1] 19 [8] 20 [3, 1, 1] 21 [4, 2] 22 [5, 1] 23 [9] 24 [2, 1, 1, 1] 25 [3, 3] 26 [6, 1] 27 [2, 2, 2] 28 [4, 1, 1] 29 [10] 30 [3, 2, 1] 31 [11] 32 [1, 1, 1, 1, 1] 33 [5, 2] 34 [7, 1] 35 [4, 3] 36 [2, 2, 1, 1] 37 [12] 38 [8, 1] 39 [6, 2] 40 [3, 1, 1, 1] 41 [13] 42 [4, 2, 1] 43 [14] 44 [5, 1, 1] 45 [3, 2, 2] 46 [9, 1] 47 [15] 48 [2, 1, 1, 1, 1] 49 [4, 4] 50 [3, 3, 1] 51 [7, 2] 52 [6, 1, 1] 53 [16] 54 [2, 2, 2, 1] 55 [5, 3] 56 [4, 1, 1, 1] 57 [8, 2] 58 [10, 1] 59 [17] 60 [3, 2, 1, 1] 61 [18] 62 [11, 1] 63 [4, 2, 2] 64 [1, 1, 1, 1, 1, 1] 65 [6, 3] 66 [5, 2, 1] 67 [19] 68 [7, 1, 1] 69 [9, 2] 70 [4, 3, 1] 71 [20] 72 [2, 2, 1, 1, 1] 73 [21] 74 [12, 1] 75 [3, 3, 2] 76 [8, 1, 1] 77 [5, 4] 78 [6, 2, 1] 79 [22] 80 [3, 1, 1, 1, 1] 81 [2, 2, 2, 2] 82 [13, 1] 83 [23] 84 [4, 2, 1, 1] 85 [7, 3] 86 [14, 1] 87 [10, 2] 88 [5, 1, 1, 1] 89 [24] 90 [3, 2, 2, 1] 91 [6, 4] 92 [9, 1, 1] 93 [11, 2] 94 [15, 1] 95 [8, 3] 96 [2, 1, 1, 1, 1, 1] 97 [25] 98 [4, 4, 1] 99 [5, 2, 2] 100 [3, 3, 1, 1] 101 [26] 102 [7,2,1] . . . ################################## e.o.f. #####################################