login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A140539 a(n) is smallest number with divisors which are congruent to 1, 2, ..., n-1 mod n. 1
1, 1, 2, 6, 8, 30, 12, 60, 96, 270, 90, 420, 72, 1638, 840, 1080, 300, 4410, 432, 5940, 3360, 6930, 540, 10920, 2880, 19890, 9360, 27300, 1680, 43890, 1200, 36720, 84480, 151470, 97440, 107100, 3780, 139650, 120120, 83160, 4800, 395850, 5040, 318780, 191520, 217350 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

n-1 <= a(n) <= A003418(n-1). - Robert Israel, Mar 08 2018

Records: 1, 2, 6, 8, 30, 60, 96, 270, 420, 1638, 4410, 5940, 6930, 10920, 19890, 27300, 43890, 84480, 151470, 395850, 546000, 1222650, 3267810, 5255250, ..., and they occur at indices: 1, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 22, 24, 26, 28, 30, 33, 34, 42, 48, 50, 54, 66, 69, 72, 75, 78, 82, 90, 96, 98, 106, 108, 126, 138, 150, 174, 180, 186, 192, 198, 210, ..., . - Robert G. Wilson v, Mar 09 2018

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..250 (first 125 terms from Andrew Weimholt)

EXAMPLE

a(7)=12: 12's divisors are 1,2,3,4,6,12 and

1 == 1 mod 7

2 == 2 mod 7

3 == 3 mod 7

4 == 4 mod 7

12 == 5 mod 7

6 == 6 mod 7

MAPLE

f:= proc(n) local k, T;

  T:= {$1..(n-1)};

  for k from n-1 do if T subset numtheory:-divisors(k) mod n then return k fi od

end proc:

map(f, [$1..50]); # Robert Israel, Mar 08 2018

MATHEMATICA

f[n_] := Block[{k = 1, m = Range[n - 1], u}, While[u = Union@ Mod[Divisors@ k, n]; If[ u[[1]] == 0, u = Rest@ u]; u != m, k++]; k]; Array[f, 46] (* Robert G. Wilson v, Mar 08 2018 *)

PROG

(PARI) a(n) = {if (n == 1, return (1)); if (n == 2, return (1)); i = 2; cref = Set(vector(n-1, k, k)); while (1, cong = Set(); fordiv (i, d, if (d % n, cong = setunion(cong, Set(d % n))); ); if (cong == cref, return (i)); i++; ); } \\ Michel Marcus, Mar 08 2013

CROSSREFS

Cf. A003418.

Sequence in context: A290423 A272614 A210737 * A056188 A020696 A290249

Adjacent sequences:  A140536 A140537 A140538 * A140540 A140541 A140542

KEYWORD

nonn

AUTHOR

Andrew Weimholt, Jul 04 2008

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 18 07:01 EST 2018. Contains 317279 sequences. (Running on oeis4.)