|
Search: id:A039770
|
|
|
| A039770 |
|
Numbers n such that phi(n) is a perfect square. |
|
+0
15
|
|
| 1, 2, 5, 8, 10, 12, 17, 32, 34, 37, 40, 48, 57, 60, 63, 74, 76, 85, 101, 108, 114, 125, 126, 128, 136, 160, 170, 185, 192, 197, 202, 204, 219, 240, 250, 257, 273, 285, 292, 296, 304, 315, 364, 370, 380, 394, 401, 432, 438, 444, 451, 456, 468, 489, 504, 505
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
REFERENCES
|
D. M. Burton, Elementary Number Theory, Allyn and Bacon Inc., Boston MA, 1976, p. 141.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..10000
W. D. Banks, J. B. Friedlander, C. Pomerance and I. E. Shparlinski, Multiplicative structure of values of the Euler function, in High Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams (A. Van der Poorten, ed.), Fields Inst. Comm. 41 (2004), pp. 29-47.
|
|
FORMULA
|
a(n) seems to be asymptotic to c*n^(3/2) with 1<c<1.3 - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 08 2002
Banks, Friedlander, Pomerance, and Shparlinski show that a(n) = O(n^1.421).
|
|
EXAMPLE
|
phi(34)=16=4*4.
|
|
MATHEMATICA
|
Select[ Range[ 600 ], IntegerQ[ Sqrt[ EulerPhi[ # ] ] ]& ]
|
|
PROGRAM
|
(PARI) for(n=1, 120, if(issquare(eulerphi(n)), print(n)))
|
|
CROSSREFS
|
Cf. A000010, A007614. A062732 gives the squares.
Sequence in context: A153052 A166955 A121294 this_sequence A047618 A059551 A126281
Adjacent sequences: A039767 A039768 A039769 this_sequence A039771 A039772 A039773
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
Olivier Gerard (olivier.gerard(AT)gmail.com)
|
|
EXTENSIONS
|
Reference and asymptotic formula from Charles R Greathouse IV (charles.greathouse(AT)case.edu), Aug 24 2009
|
|
|
Search completed in 0.002 seconds
|
