login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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