A071008 Numbers n such that uphi(uphi(n)) = n/2.

2, 4, 16, 256, 364, 1456, 3276, 13104, 21600, 23296, 65536, 209664, 249984, 367200, 1285632, 3110400, 5963776, 6596304, 9749376, 23046144, 27216000, 33022080, 52876800, 53673984, 76639680, 94370400, 105540864, 119992320, 245765520, 285405120, 426037248

Offset: 1

Author

Yasutoshi Kohmoto

Keywords

• nonn

Comments

If n = Product p_i^r_i then uphi(n) = Product (p_i^r_i-1); for example uphi(12) = (4-1)*(3-1) = 6.

If 2^n+1 is a Fermat prime then 2^(2*n) is a solution of the equation.

3110400 and 4294967296 are also in the sequence.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..41 (terms < 2^35)

Crossrefs

Cf. A030163, A047994.

Programs

PARI

forstep(n=2,1e9,2,A047994(A047994(n))*2-n || print1(n", ")) \\ M. F. Hasler, Nov 20 2010

Formula

{n: 2*A047994(A047994(n)) = n}.

Extensions

More terms from R. J. Mathar, Alois P. Heinz and M. F. Hasler, Nov 20 2010