1,1

Note that if Phi[x] = n!, then x must be a product of primes p such that p - 1 divides n!. - David Wasserman (wasserma(AT)spawar.navy.mil), Apr 30 2002

Gives the row lengths of the table A165773 (see example). It seems that all solutions to phi(x)=n! are in the interval [n!,(n+1)! ], the smallest resp. largest solutions being given in A055487 resp. A165774. See there for more details. [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 04 2009]

a(n) = A014197(n!) = Cardinality[{x; A000010(x) = A000142(n)}]

n = 5, Phi[x] = 5! = 120 holds for the following 17 numbers: {143,155,175,183,225,231,244,248,286,308,310,350,366,372,396,450,462}

Contribution from M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 04 2009: (Start)

The table A165773 looks as follows:

1,2, /* A055506(1)=2 numbers for which phi(n) = 1! = 1 */

3,4,6, /* A055506(2)=3 numbers for which phi(n) = 2! = 2 */

7,9,14,18, /* A055506(3)=4 numbers for which phi(n) = 3! = 6 */

35,39,45,52,56,70,72,78,84,90, /* A055506(4)=10 numbers for which phi(n) = 4! = 24 */

143,155,175,183,225,231,244,248,286,308,310,350,366,372,396,450,462, /* A055506(5)=17 numbers for which phi(n) = 5! = 120 */ (End)

Cf. A000142, A000010, A014197, A000203, A054873, A067847, A055486.

Sequence in context: A115899 A085934 A056701 this_sequence A098088 A080500 A007661

Adjacent sequences: A055503 A055504 A055505 this_sequence A055507 A055508 A055509

nonn

Labos E. (labos(AT)ana.sote.hu), Jun 29 2000

More terms from Jud McCranie (j.mccranie(AT)comcast.net), Jan 02 2001

More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Apr 30 2002 (with the assistance of Vladeta Jovovic and Sascha Kurz).