A145190 Numbers k such that phi(1)*phi(2)*...*phi(k) / k is an integer, where phi(k) is the totient function (A000010).

1, 4, 8, 9, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 65, 66, 69, 70, 72, 75, 77, 78, 80, 81, 84, 87, 88, 90, 91, 92, 96, 98, 99, 100, 104, 105, 108, 110, 112, 115, 116, 117, 119, 120, 121, 123

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

Select[Range[200], IntegerQ[Product[EulerPhi[i], {i, 1, #}]/#] &] (* Carl Najafi, Aug 19 2011 *)
nn=150; With[{ep=Rest[FoldList[Times, 1, EulerPhi[Range[nn]]]]}, Flatten[ Position[Table[ep[[i]]/i, {i, nn}], _?IntegerQ]]] (* Harvey P. Dale, May 12 2012 *) (* this program is more than 200 times faster than the first Mathematica program above *)

Prog

(PARI) isok(n)=prod(k=1, n, eulerphi(k))%n==0 \\ Anders Hellström, Aug 22 2015

Crossrefs

Cf. A000010, A048290, A144857.

Sequence in context: A291791 A037973 A044844 * A327907 A177713 A235992

Adjacent sequences: A145187 A145188 A145189 * A145191 A145192 A145193

Keyword

easy,nonn

Author

Ctibor O. Zizka, Oct 03 2008

Extensions

More terms from Carl Najafi, Aug 19 2011

Status

approved