A002181 Least number k such that phi(k) = m, where m runs through the values (A002202) taken by phi.

1, 3, 5, 7, 15, 11, 13, 17, 19, 25, 23, 35, 29, 31, 51, 37, 41, 43, 69, 47, 65, 53, 81, 87, 59, 61, 85, 67, 71, 73, 79, 123, 83, 129, 89, 141, 97, 101, 103, 159, 107, 109, 121, 113, 177, 143, 127, 255, 131, 161, 137, 139, 213, 185, 149, 151, 157, 187, 163, 249, 167, 203, 173

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Inverse of Euler totient function.

A051445 without the zeros. The values of m are in A002180.

According to Guy, the first even term is for 2m = 16842752 = 257*2^16. If there are only five Fermat primes, then terms will be even for 2m = 2^r for all r > 31. This was discussed in problem E3361. - T. D. Noe, Aug 14 2008

References

• J. W. L. Glaisher, Number-Divisor Tables. British Assoc. Math. Tables, Vol. 8, Camb. Univ. Press, 1940, p. 64.
• R. K. Guy, Unsolved problems in number theory, B39.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• R. D. Carmichael, A table of the values of m corresponding to given values of phi(m), Amer. J. Math., 30 (1908), 394-400. [Annotated scanned copy]
• T. D. Noe, Numbers Like 16842752.
• William P. Wardlaw, L. L. Foster and R. J. Simpson, Problem E3361, Amer. Math. Monthly, Vol. 98, No. 5 (May, 1991), 443-444.
• K. W. Wegner, Values of phi(x) = n for n from 2 through 1978, mimeographed manuscript, no date [Annotated scanned copy]

Crossrefs

Cf. A058277, A006511, A002202, A061026.

Programs

Mathematica

With[{ep=EulerPhi[Range[1000]]},Flatten[Table[Position[ep,n,{1},1],{n,200}]]] (* Harvey P. Dale, Apr 10 2015 *)

Formula

a(n) = A061026(A002202(n)). - Flávio V. Fernandes, Oct 08 2023

Extensions

Offset and initial term corrected Oct 07 2007

Revised definition from T. D. Noe, Aug 14 2008