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

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, 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, 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

Offset

1,4

Links

Table of n, a(n) for n=1..94.

Example

a(19)=5 because
f(19) = 19 - tau(sigma(19)) = 19 - tau(20) = 19 - 6 = 13;
f(13) = 13 - tau(sigma(13)) = 13 - tau(14) = 13 - 4 = 9;
f(9) = 9 - tau(sigma(9)) = 9 - tau(13) = 9 - 2 = 7;
f(7) = 7- tau(sigma(7)) = 7 - tau(8) = 7 - 4 = 3;
f(3) = 3- tau(sigma(3)) = 3 - tau(4) = 3 - 3 = 0;

Maple

A062068 := proc(n)
        numtheory[tau](numtheory[sigma](n)) ;
end proc:
A176816 := proc(n)
        a := 0 ;
        x := n ;
        while x <> 0 do
                x := x-A062068(x) ;
                a := a+1 ;
        end do:
        a ;
end proc: # R. J. Mathar, Oct 11 2011

Mathematica

f[n_] := If[n == 0, 0, n - DivisorSigma[0, DivisorSigma[1, n]]];
a[n_] := Length[FixedPointList[f, n]] - 2;
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Apr 09 2024 *)

Crossrefs

Cf. A062068.

Sequence in context: A165927 A127830 A371275 * A053284 A050371 A172313

Adjacent sequences: A176813 A176814 A176815 * A176817 A176818 A176819

Keyword

nonn

Author

Michel Lagneau, Apr 26 2010

Status

approved