A290149 Totient sublime numbers: numbers k such that the number of terms in the iterations of phi(k) from k to 1, A032358(k)+2, and their sum, A092693(k) are both perfect totient numbers (A082897).

6, 2916, 4374, 109100, 113708, 3188646

Offset

1,1

Comments

Analogous to A081357 (sublime numbers), as A082897 (perfect totient numbers) is analogous to A000396 (perfect numbers).

No other terms below 10^8.

Links

Table of n, a(n) for n=1..6.

Example

There are 9 terms in the iterations of phi(k) for 2916: 2916, 972, 324, 108, 36, 12, 4, 2, 1. Their sum is 4375. Both 9 and 4375 are perfect totient numbers (A082897).

Mathematica

iterList [n_] := FixedPointList[EulerPhi@# &, n]; sumIter [n_] := Plus @@ iterList[n] - 1; numIter[n_] := Length[iterList[n]] - 1; perfTotQ[n_] := sumIter[n] == 2 n; totSublimeQ[n_] := perfTotQ[numIter[n]] && perfTotQ[sumIter[n]]; Select[Range [10^8], totSublimeQ]

Crossrefs

Cf. A032358, A081357, A082897, A092693.

Sequence in context: A001326 A300851 A089501 * A187083 A114184 A093884

Adjacent sequences: A290146 A290147 A290148 * A290150 A290151 A290152

Keyword

nonn,more

Author

Amiram Eldar, Jul 21 2017

Status

approved