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A176816 The number of steps to reach 0 under the map x -> x-tau(sigma(x)), starting at n. 1

%I

%S 1,1,1,2,2,1,2,3,3,3,3,2,4,2,3,3,4,3,5,3,4,5,4,3,5,4,6,4,5,4,6,5,5,5,

%T 6,6,6,5,7,5,6,5,7,6,7,6,7,6,8,7,8,7,8,6,8,6,8,7,8,7,9,8,9,9,9,9,10,7,

%U 9,9,9,10,10,10,10,10,10,9,10,11,10,10,10,11,11,11,10,10,11,10,11,11,12,11

%N The number of steps to reach 0 under the map x -> x-tau(sigma(x)), starting at n.

%e a(19)=5 because

%e f(19) = 19 - tau(sigma(19)) = 19 - tau(20) = 19 - 6 = 13;

%e f(13) = 13 - tau(sigma(13)) = 13 - tau(14) = 13 - 4 = 9;

%e f(9) = 9 - tau(sigma(9)) = 9 - tau(13) = 9 - 2 = 7;

%e f(7) = 7- tau(sigma(7)) = 7 - tau(8) = 7 - 4 = 3;

%e f(3) = 3- tau(sigma(3)) = 3 - tau(4) = 3 - 3 = 0;

%p A062068 := proc(n)

%p numtheory[tau](numtheory[sigma](n)) ;

%p end proc:

%p A176816 := proc(n)

%p a := 0 ;

%p x := n ;

%p while x <> 0 do

%p x := x-A062068(x) ;

%p a := a+1 ;

%p end do:

%p a ;

%p end proc: # _R. J. Mathar_, Oct 11 2011

%Y Cf. A062068.

%K nonn

%O 1,4

%A _Michel Lagneau_, Apr 26 2010

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Last modified October 22 13:49 EDT 2021. Contains 348170 sequences. (Running on oeis4.)