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 A176841 a(n) is the number of iterations of f(n) = n-phi(tau(n)) needed to reach 1. 1
 0, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 7, 8, 8, 9, 9, 10, 10, 11, 10, 12, 11, 13, 12, 13, 12, 13, 13, 14, 14, 15, 13, 14, 14, 15, 14, 15, 15, 16, 16, 17, 17, 18, 17, 19, 18, 20, 19, 20, 19, 21, 20, 22, 21, 22, 21, 22, 22, 23, 22, 24, 23, 24, 24, 25, 24, 25, 25, 26, 26, 27, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS tau(n) is the number of divisors of n (A000005) and phi(n) is the Euler totient function (A000010). REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE for n = 13, the number 7 is in the sequence because : f(13) = 13 - phi(tau(13)) = 13 - phi(2) = 13 - 1 = 12; f(12) = 12 - phi(tau(12)) = 12 - phi(6) = 12 - 2 = 10; f(10) = 10 - phi(tau(10)) = 10 - phi(4) = 10 - 2 = 8; f(8) = 8- phi(tau(8)) = 8 - phi(4) = 8 - 2 = 6 ; f(6) = 6- phi(tau(6)) = 6 - phi(4) = 6 - 2 = 4 ; f(4) = 4- phi(tau(4)) = 4 - phi(3) = 4 - 2 = 2 ; f(2) = 2- phi(tau(2)) = 2 - phi(2) = 2 - 1 = 1, and a(13) = 7. MAPLE with(numtheory): n0:=200:tabl:=array(1..n0): for n from 1 to 1000 do:k:=0:nn:=n:for q from 0 to 1000 while(nn<>1) do:nn:=nn - phi(tau((nn))):k:=k+1:od:tabl[n]:=k:od:print(tabl): MATHEMATICA f[n_] := (k++; n - EulerPhi[ DivisorSigma[0, n]]); f[0] = 0; a[n_] := (k=0; FixedPoint[f, n]; k-1); Table[a[n], {n, 1, 76}](* Jean-François Alcover, May 10 2012 *) CROSSREFS Cf. A000005, A000010. Sequence in context: A238263 A071542 A264810 * A176814 A088461 A135020 Adjacent sequences:  A176838 A176839 A176840 * A176842 A176843 A176844 KEYWORD nonn AUTHOR Michel Lagneau, Apr 27 2010 STATUS approved

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Last modified May 30 05:35 EDT 2020. Contains 334712 sequences. (Running on oeis4.)