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A124240 Numbers n such that lambda(n) divides n, where lambda is Carmichael's function (A002322). 21
1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 32, 36, 40, 42, 48, 54, 60, 64, 72, 80, 84, 96, 100, 108, 120, 126, 128, 144, 156, 160, 162, 168, 180, 192, 200, 216, 220, 240, 252, 256, 272, 288, 294, 300, 312, 320, 324, 336, 342, 360, 378, 384, 400, 420, 432, 440, 468, 480 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that A124239(n) is divisible by n.

If k is in the sequence then 2k is also in the sequence, but if 2m is in the sequence m is not necessarily a term of the sequence.

This sequence is a subsequence of A068563. The first term that is different is A068563(27) = 136. The terms of A068563 that are not the terms of a(n) are listed in A124241.

Also, the sequence of numbers n such that p-1 divides n for all primes p that divide n. - Leroy Quet, Jun 27 2008.

Numbers n such that b^n == 1 (mod n) for every b coprime to n. - Thomas Ordowski, Jun 23 2017

Numbers m such that every divisor < m is the difference between two divisors of m. - Michel Lagneau, Aug 11 2017

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

Alexander Kalmynin, On Novák numbers, arXiv:1611.00417 [math.NT], 2016. See Theorem 6 p. 11 where these numbers are called Novák-Carmichael numbers.

Eric Weisstein's World of Mathematics, Carmichael Function

EXAMPLE

a(1) = 1 because 1 divides A124239(1) = 1.

a(2) = 2 because 2 divides A124239(2) = 14.

a(3) = 4 because 4 divides A124239(4) = 3704, but 3 does not divide A124239(3) = 197.

MAPLE

A124240:= proc(i, k) local a, n, ok; print(1);

for n from k+1 to i do ok:=1;

  for a from 0 to n do

     if gcd(a, n)=1 then  if (a^(n-k) mod n)<>1 then ok:=0; break; fi; fi; od;

  if ok=1 then print(n); fi; od; end:

A124240(1000, 0); # Paolo P. Lava, Apr 19 2013

MATHEMATICA

Do[f=n + Sum[ (2k-1)((2k-1)^n-1) / (2(k-1)), {k, 2, n} ]; If[IntegerQ[f/n], Print[n]], {n, 1, 900}]

Flatten[Position[Table[n/CarmichaelLambda[n], {n, 440}], _Integer]] (* T. D. Noe, Sep 11 2008 *)

PROG

(Haskell)

a124240 n = a124240_list !! (n-1)

a124240_list = filter

   (\x -> all (== 0) $ map ((mod x) . pred) $ a027748_row x) [1..]

-- Reinhard Zumkeller, Aug 27 2013

(PARI) is(n)=n%lcm(znstar(n)[2])==0 \\ Charles R Greathouse IV, Feb 11 2015

CROSSREFS

Cf. A002322, A124239, A124241, A068563, A027748, A140470, A141766.

Sequence in context: A177807 A305726 A068563 * A320580 A325763 A068997

Adjacent sequences:  A124237 A124238 A124239 * A124241 A124242 A124243

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Oct 22 2006

EXTENSIONS

New definition from T. D. Noe, Aug 31 2008

Edited by Max Alekseyev, Aug 25 2013

STATUS

approved

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Last modified December 10 00:54 EST 2019. Contains 329885 sequences. (Running on oeis4.)