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A225172
Largest number which requires n iterations of the unitary totient function (A047994) to reach 1.
5
1, 2, 6, 14, 42, 86, 186, 462, 930, 1986, 4170, 6510, 14682, 29366, 50342, 73410, 189498, 287654, 491190, 849570, 1699142, 2433878, 4280774, 7978218, 14442690, 25900142, 44400390, 78492954, 123958794, 228018066, 355388970, 629582370, 780686294
OFFSET
0,2
COMMENTS
Searched up to 10^10. a(33) >= 1609056138. a(34) >= 2275537110. a(35) >= 4171607222. - Donovan Johnson, May 02 2013
LINKS
FORMULA
a(n) = max{ x : A049865(x) = n} - R. J. Mathar, May 02 2013
MATHEMATICA
(* This is just a verification of recorded data up to a(23), assuming a(n-1)/2 <= a(n) <= 4*a(n-1) *) uphi[n_] := (cnt++; fi = FactorInteger[n]; Times @@ (fi[[All, 1]]^fi[[All, 2]] - 1)); f[n_] := (cnt = 0; NestWhile[uphi, n, # > 1 &]; cnt); a[0] = 1; a[1] = 2; a[n_] := a[n] = For[record = k = a[n-1]/2//Floor, k <= 4*a[n-1], k++, If[f[k] == n, record = k]]; record); Table[Print[a[n]]; a[n], {n, 0, 23}] (* Jean-François Alcover, May 02 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 01 2013
EXTENSIONS
a(16)-a(32) from Donovan Johnson, May 02 2013
STATUS
approved