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. #####################################