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A055506
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Number solutions to the equation phi(x) = n!.
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4
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2, 3, 4, 10, 17, 49, 93, 359, 1138, 3802, 12124, 52844, 182752, 696647, 2852886, 16423633, 75301815, 367900714, 1531612895, 8389371542, 40423852287, 213232272280, 1295095864798, 7991762413764, 42259876674716, 252869570952706, 1378634826630301
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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). All solutions to phi(x)=n! are in the interval [n!,(n+1)!] with the smallest/largest solutions given in A055487/A165774 respectively. [From M. F. Hasler (www.univ-ag.fr/~mhasler), Oct 04 2009]
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FORMULA
| a(n) = A014197(n!) = Cardinality[{x; A000010(x) = A000142(n)}]
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EXAMPLE
| 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 (www.univ-ag.fr/~mhasler), Oct 04 2009: (Start)
The table A165773 looks as follows:
1,2, /* a(1)=2 numbers for which phi(n) = 1! = 1 */
3,4,6, /* a(2)=3 numbers for which phi(n) = 2! = 2 */
7,9,14,18, /* a(3)=4 numbers for which phi(n) = 3! = 6 */
35,39,45,52,56,70,72,78,84,90, /* a(4)=10 numbers for which phi(n) = 4! = 24 */ (End)
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CROSSREFS
| Cf. A000142, A000010, A014197, A000203, A054873, A067847, A055486, A165774
Sequence in context: A183527 A085934 A056701 * A098088 A080500 A007661
Adjacent sequences: A055503 A055504 A055505 * A055507 A055508 A055509
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jun 29 2000
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EXTENSIONS
| More terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), 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).
a(21)-a(27) from Max Alekseyev (maxale(AT)gmail.com), Jan 26 2012
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