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 A334184 Irregular table read by rows: T(n,k) gives the number of values that can be reached after exactly k iterations of maps of the form (n - n/p) where p is a prime divisor of n. 0 <= k < A073933(n). 9
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,15 COMMENTS Row lengths are given by A073933(n). Row sums are given by A332809(n). The maximum value in each row is given by A334144(n). The n-th row consists of all 1's if and only if n is a power of two (A000079) or a Fermat prime (A019434). Conjecture: rows are unimodal (increasing and then decreasing). Not all rows are unimodal. Indices of rows that have terms that increase and decrease more than once are A334238. - Michael De Vlieger, Apr 18 2020 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..12386 (rows 1 <= n <= 1000, flattened) Michael De Vlieger, Hasse diagrams showing rows n = {55, 63, 171, ...} that increase and decrease more than once. Michael De Vlieger, Table of n, b(n) for n = 1..10000, encoding the running total of row n of this sequence as a binary number expressed decimally. FORMULA T(n,0) = T(n, A073933(n) - 2) = T(n, A073933(n) - 1) = 1. T(n,1) = A001221(n) for n > 1. EXAMPLE For n = 15, the fifteenth row of this table is [1,2,3,2,1,1] because there is one value (15 itself) that can be reached with zero iterations of (n - n/p) maps, two values (10 and 12) that can be reached after one iteration, three values (5, 8, and 6) that can be reached after two iterations, and so on.       15      _/ \_     /     \   10       12   | \_   _/ |   |   \ /   |   5    8    6    \_  |  _/|      \_|_/  |        4    3        |  _/        |_/        2        |        |        1 Table begins: 1 1, 1 1, 1, 1 1, 1, 1 1, 1, 1, 1 1, 2, 1, 1 1, 1, 2, 1, 1 1, 1, 1, 1 1, 1, 2, 1, 1 1, 2, 1, 1, 1 1, 1, 2, 1, 1, 1 1, 2, 2, 1, 1 1, 1, 2, 2, 1, 1 1, 2, 2, 2, 1, 1 1, 2, 3, 2, 1, 1 1, 1, 1, 1, 1 MATHEMATICA Table[Length@ Union@ # & /@ Transpose@ # &@ If[n == 1, {{1}}, NestWhile[If[Length[#] == 0, Map[{n, #} &, # - # /FactorInteger[#][[All, 1]] ], Union[Join @@ Map[Function[{w, n}, Map[Append[w, If[n == 0, 0, n - n/#]] &, FactorInteger[n][[All, 1]] ]] @@ {#, Last@ #} &, #]]] &, n, If[ListQ[#], AllTrue[#, Last[#] > 1 &], # > 1] &]], {n, 22}] // Flatten (* Michael De Vlieger, Apr 18 2020 *) CROSSREFS Cf. A001221, A073933, A332809, A333123, A334111, A334144, A334238. Cf. A000079, A019434. Sequence in context: A136441 A030561 A202053 * A249545 A296081 A074064 Adjacent sequences:  A334181 A334182 A334183 * A334185 A334186 A334187 KEYWORD nonn,tabf AUTHOR Peter Kagey, Apr 17 2020 STATUS approved

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Last modified May 17 09:03 EDT 2021. Contains 343969 sequences. (Running on oeis4.)