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Numbers n for which phi(n) = m! for some integer m, where phi = A000010.
4

%I #7 Jul 14 2012 11:32:32

%S 1,2,3,4,6,7,9,14,18,35,39,45,52,56,70,72,78,84,90,143,155,175,183,

%T 225,231,244,248,286,308,310,350,366,372,396,450,462,779,793,803,905,

%U 925,1001,1045,1085,1107,1209,1221,1281,1287,1395,1425,1448,1485,1558,1575

%N Numbers n for which phi(n) = m! for some integer m, where phi = A000010.

%C A subsequence of A032447. Can be read as "fuzzy" table, where the m-th row contains A055506(m) numbers with phi=m!, ranging from A055487(m) to A165774(m). See there for more information.

%C A log-log plot shows the components of this sequence better. - _T. D. Noe_, Jun 21 2012

%H T. D. Noe, <a href="/A165773/b165773.txt">Table of n, a(n) for n = 1..5477</a> (for factorials up to 10)

%H T. D. Noe, <a href="/A165773/a165773.png">A log-log plot</a>

%e The table looks as follows:

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

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

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

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

%e 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 */ ...

%o (PARI) for(m=1,8, for( n=f=m!,f*(m+1), eulerphi(n)==f & print1(n","));print())

%K nonn,tabf

%O 1,2

%A _M. F. Hasler_, Oct 02 2009

%E Fixed references to A055506, A055487 and A165774 - M. F. Hasler, Oct 04 2009