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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007617 Values not in range of Euler phi function. 31
3, 5, 7, 9, 11, 13, 14, 15, 17, 19, 21, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 45, 47, 49, 50, 51, 53, 55, 57, 59, 61, 62, 63, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 98, 99, 101, 103, 105, 107 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Nontotient numbers.

All odd numbers > 2 are in the sequence.

The even numbers of the sequence are in A005277.

A264739(a(n)) = 0. - Reinhard Zumkeller, Nov 26 2015

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, B36.

LINKS

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

Jerzy Browkin and Andrzej Schinzel, On integers not of the form n-phi(n), Colloq. Math., 58 (1995) 55-58.

P. Erdős and R. R. Hall, Distinct values of Euler's phi-function, Mathematika, 23 (1976) 1-3.

Kevin Ford, The distribution of totients. Paul Erdős (1913-1996). Ramanujan J., 2 (1998) 67-151.

Kevin Ford, The distribution of totients, Electron. Res. Announc. Amer. Math. Soc., 4 (1998) 27-34.

Kevin Ford, The distribution of totients, arXiv:1104.3264 [math.NT], 2011-2013.

Kevin Ford, The number of solutions of phi(x)=m, Ann. of Math.(2), 150 (1999) 283-311.

Helmut Maier and Carl Pomerance, On the number of distinct values of Euler's phi-function, Acta Arithmetica 49:3 (1988), pp. 263-275.

Maxim Rytin, Finding the Inverse of Euler Totient Function (1999).

Zhang Ming-Zhi, On nontotients, J. Number Theory, 43 (1993) 168-173.

EXAMPLE

There are no solutions to phi(m)=14, so 14 is a member of the sequence.

MAPLE

A007617 := n -> if invphi(n)=[] then n fi: seq(A007617(i), i=1..107); # Peter Luschny, Jun 26 2011

MATHEMATICA

inversePhi[m_?OddQ] = {}; inversePhi[1] = {1, 2}; inversePhi[m_] := Module[{p, nmax, n, nn}, p = Select[Divisors[m] + 1, PrimeQ]; nmax = m*Times @@ (p/(p - 1)); n = m; nn = {}; While[n <= nmax, If[EulerPhi[n] == m, AppendTo[nn, n]]; n++]; nn]; Select[Range[107], inversePhi[#] == {} &] (* Jean-François Alcover, Jan 03 2012 *)

Select[Range[107], invphi[#] == {}&] (* Jean-François Alcover, Mar 19 2019, using Maxim Rytin's much faster 'invphi' program *)

PROG

(PARI) is(n)=!istotient(n) \\ Charles R Greathouse IV, Dec 28 2013

(Haskell)

import Data.List.Ordered (minus)

a007617 n = a007617_list !! (n-1)

a007617_list = [1..] `minus` a002202_list

-- Reinhard Zumkeller, Nov 22 2015

CROSSREFS

Numbers not in A000010.

Cf. A002202, A005277, A180639.

Cf. A083534 (first differences), A264739.

Sequence in context: A097218 A196546 A231773 * A065878 A186383 A284055

Adjacent sequences:  A007614 A007615 A007616 * A007618 A007619 A007620

KEYWORD

nonn

AUTHOR

Walter Nissen

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 November 18 09:46 EST 2019. Contains 329261 sequences. (Running on oeis4.)