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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). 0
6, 2916, 4374, 109100, 113708, 3188646 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 22 10:56 EDT 2022. Contains 353949 sequences. (Running on oeis4.)