Search: id:A055506
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%I A055506
%S A055506 2,3,4,10,17,49,93,359,1138,3802,12124,52844,182752,696647,2852886,
%T A055506 16423633,75301815,367900714,1531612895,8389371542
%N A055506 Number of x with EulerPhi[x] = n!.
%C A055506 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
%C A055506 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]
%F A055506 a(n) = A014197(n!) = Cardinality[{x; A000010(x) = A000142(n)}]
%e A055506 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}
%e A055506 Contribution from M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 04 2009: 
               (Start)
%e A055506 The table A165773 looks as follows:
%e A055506 1,2, /* A055506(1)=2 numbers for which phi(n) = 1! = 1 */
%e A055506 3,4,6, /* A055506(2)=3 numbers for which phi(n) = 2! = 2 */
%e A055506 7,9,14,18, /* A055506(3)=4 numbers for which phi(n) = 3! = 6 */
%e A055506 35,39,45,52,56,70,72,78,84,90, /* A055506(4)=10 numbers for which phi(n) 
               = 4! = 24 */
%e A055506 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)
%Y A055506 Cf. A000142, A000010, A014197, A000203, A054873, A067847, A055486.
%Y A055506 Sequence in context: A115899 A085934 A056701 this_sequence A098088 A080500 
               A007661
%Y A055506 Adjacent sequences: A055503 A055504 A055505 this_sequence A055507 A055508 
               A055509
%K A055506 nonn
%O A055506 1,1
%A A055506 Labos E. (labos(AT)ana.sote.hu), Jun 29 2000
%E A055506 More terms from Jud McCranie (j.mccranie(AT)comcast.net), Jan 02 2001
%E A055506 More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Apr 30 
               2002 (with the assistance of Vladeta Jovovic and Sascha Kurz).

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