A165773 Numbers n for which phi(n) = m! for some integer m, where phi = A000010.

1, 2, 3, 4, 6, 7, 9, 14, 18, 35, 39, 45, 52, 56, 70, 72, 78, 84, 90, 143, 155, 175, 183, 225, 231, 244, 248, 286, 308, 310, 350, 366, 372, 396, 450, 462, 779, 793, 803, 905, 925, 1001, 1045, 1085, 1107, 1209, 1221, 1281, 1287, 1395, 1425, 1448, 1485, 1558, 1575

Offset: 1

Author

M. F. Hasler, Oct 02 2009

Keywords

• nonn
• tabf

Comments

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.

A log-log plot shows the components of this sequence better. - T. D. Noe, Jun 21 2012

Examples

			The table 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 */ ...
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..5477 (for factorials up to 10)
• T. D. Noe, A log-log plot

Programs

PARI

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

Extensions

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