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
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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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 *) -
PARI
isok(n)=prod(k=1,n,eulerphi(k))%n==0 \\ Anders Hellström, Aug 22 2015
Extensions
More terms from Carl Najafi, Aug 19 2011