login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A298882 a(1) = 1, and for any n > 1, if n is the k-th number with least prime factor p, then a(n) is the k-th number with greatest prime factor p. 1
1, 2, 3, 4, 5, 8, 7, 16, 6, 32, 11, 64, 13, 128, 9, 256, 17, 512, 19, 1024, 12, 2048, 23, 4096, 10, 8192, 18, 16384, 29, 32768, 31, 65536, 24, 131072, 15, 262144, 37, 524288, 27, 1048576, 41, 2097152, 43, 4194304, 36, 8388608, 47, 16777216, 14, 33554432, 48 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is a permutation of the natural numbers, with inverse A298268.

For any prime p and k > 0:

- if s_p(k) is the k-th p-smooth number and r_p(k) is the k-th p-rough number,

- then a(p * r_p(k)) = p * s_p(k),

- for example: a(11 * A008364(k)) = 11 * A051038(k).

LINKS

Table of n, a(n) for n=1..51.

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(1) = 1.

a(A083140(n, k)) = A125624(n, k) for any n > 0 and k > 0.

a(n) = A125624(A055396(n), A078898(n)) for any n > 1.

Empirically:

- a(n) = n iff n belongs to A046022,

- a(2 * k) = 2^k for any k > 0,

- a(p^2) = 2 * p for any prime p,

- a(p * q) = 3 * p for any pair of consecutive odd primes (p, q).

EXAMPLE

The first terms, alongside A020639(n), are:

  n     a(n)    lpf(n)

  --    ----    ------

   1       1      1

   2       2      2

   3       3      3

   4       4      2

   5       5      5

   6       8      2

   7       7      7

   8      16      2

   9       6      3

  10      32      2

  11      11     11

  12      64      2

  13      13     13

  14     128      2

  15       9      3

  16     256      2

  17      17     17

  18     512      2

  19      19     19

  20    1024      2

CROSSREFS

Cf. A008364, A020639, A046022, A051038, A055396, A078898, A083140, A125624, A298268 (inverse).

Sequence in context: A075162 A056240 A069968 * A086931 A243405 A164339

Adjacent sequences:  A298879 A298880 A298881 * A298883 A298884 A298885

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Jan 28 2018

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 January 18 10:47 EST 2022. Contains 350454 sequences. (Running on oeis4.)