

A002181


Least number k such that phi(k) = n, where n runs through the values (A002202) taken by phi.
(Formerly M2421 N0957)


13



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Inverse of Euler totient function.
A051445 without the zeros. The values of n are in A002180.
According to Guy, the first even term is for 2n = 16842752 = 257*2^16. If there are only five Fermat primes, then terms will be even for 2n = 2^r for all r > 31. This was discussed in problem E3361. [T. D. Noe, Aug 14 2008]


REFERENCES

J. W. L. Glaisher, NumberDivisor 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),394400. [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), 443444.
K. W. Wegner, Values of phi(x) = n for n from 2 through 1978, mimeographed manuscript, no date [Annotated scanned copy]


MATHEMATICA

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


CROSSREFS

Cf. A058277, A006511.
Sequence in context: A061390 A227685 A051445 * A073692 A132012 A160690
Adjacent sequences: A002178 A002179 A002180 * A002182 A002183 A002184


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Offset and initial term corrected Oct 07 2007
Revised definition from T. D. Noe, Aug 14 2008


STATUS

approved



