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A036913 Sparsely totient numbers; numbers n such that m > n implies phi(m) > phi(n). 9
2, 6, 12, 18, 30, 42, 60, 66, 90, 120, 126, 150, 210, 240, 270, 330, 420, 462, 510, 630, 660, 690, 840, 870, 1050, 1260, 1320, 1470, 1680, 1890, 2310, 2730, 2940, 3150, 3570, 3990, 4620, 4830, 5460, 5610, 5670, 6090, 6930, 7140, 7350, 8190, 9240, 9660 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The paper by Masser and Shiu lists 150 terms of this sequence less than 10^6. For odd prime p, they show that p# and p*p# are in this sequence, where p# denotes the primorial (A002110). - T. D. Noe, Jun 14 2006

LINKS

T. D. Noe, Table of n, a(n) for n = 1..5000

Roger C. Baker and Glyn Harman, Sparsely totient numbers, Annales de la Faculté des Sciences de Toulouse Ser. 6, 5 no. 2 (1996), 183-190.

Glyn Harman, On sparsely totient numbers, Glasgow Math. J. 33 (1991), 349-358.

D. W. Masser and P. Shiu, On sparsely totient numbers, Pacific J. Math. 121, no. 2 (1986), 407-426.

Michael De Vlieger, Largest k such that A002110(k) | a(n) and A287352(a(n)).

Michael De Vlieger, First term m > prime(n)^2 in A036913 such that gcd(prime(n), m) = 1.

EXAMPLE

This sequence contains 60 because of all the numbers whose totient is <=16, 60 is the largest such number. [From Graeme McRae, Feb 12 2009]

From Michael De Vlieger, Jun 25 2017: (Start)

Positions of primorials A002110(k) in a(n):

     n     k       a(n) = A002110(k)

  ----------------------------------

     1     1                       2

     2     2                       6

     5     3                      30

    13     4                     210

    31     5                    2310

    69     6                   30030

   136     7                  510510

   231     8                 9699690

   374     9               223092870

   578    10              6469693230

   836    11            200560490130

  1169    12           7420738134810

  1591    13         304250263527210

  2149    14       13082761331670030

  2831    15      614889782588491410

  3667    16    32589158477190044730

  4661    17  1922760350154212639070

(End)

MATHEMATICA

nn=10000; lastN=Table[0, {nn}]; Do[e=EulerPhi[n]; If[e<=nn, lastN[[e]]=n], {n, 10nn}]; mx=0; lst={}; Do[If[lastN[[i]]>mx, mx=lastN[[i]]; AppendTo[lst, mx]], {i, Length[lastN]}]; lst - T. D. Noe, Jun 14 2006

Union@ FoldList[Max, Values[#][[All, -1]]] &@ KeySort@ PositionIndex@ EulerPhi@ Range[10^4] (* Michael De Vlieger, Jun 06 2017, Version 10 *)

CROSSREFS

Cf. A097942 (highly totient numbers). Records in A006511 (see also A132154).

Sequence in context: A006511 A113274 A181660 * A117311 A125024 A178480

Adjacent sequences:  A036910 A036911 A036912 * A036914 A036915 A036916

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified July 25 15:34 EDT 2017. Contains 289795 sequences.