A256122 Number of iterations needed to reach 0 or 1 under the map n-> n-sopf(n), where sopf(n) is the sum of the distinct primes dividing n (A008472).

0, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 3, 1, 2, 3, 2, 3, 2, 1, 3, 1, 4, 2, 3, 2, 2, 1, 2, 2, 3, 1, 4, 1, 2, 2, 3, 1, 2, 5, 2, 2, 2, 1, 6, 3, 2, 3, 4, 1, 3, 1, 2, 2, 3, 2, 3, 1, 6, 2, 3, 1, 2, 1, 3, 2, 4, 2, 4, 1, 2, 5, 3, 1, 3, 3, 2, 4

Offset

1,4

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Example

a(16) = 3 because:
16 - sopf(16) = 16 - 2 = 14 (first iteration);
14 - sopf(14) = 14 - 9 = 5 (second iteration);
5 - sopf(5)= 5 - 5 = 0 (third iteration and reaching 0).
a(22) = 3 because:
22 - sopf(22) = 22 - 13 = 9 (first iteration);
9 - sopf(9) = 9 - 3 = 6 (second iteration);
6 - sopf(6)= 6 - 5 = 1 (third iteration and reaching 1).

Maple

A008472:= n -> add(d, d = select(isprime, numtheory[divisors](n))):
  A:= proc(n)
        a := 0 ;
        x := n ;
        while x>1 do
                x := x-A008472(x) ;
                a := a+1 ;
        end do:
        a ;
end proc:
seq(A(n), n=1..100);

Mathematica

t[n_] := -1 + Length[NestWhileList[#-Total[Transpose[FactorInteger[#]][[1]]]&, n, #>1&]]; Table[t[n], {n, 100}]

Crossrefs

Cf. A008472.

Sequence in context: A069010 A353332 A353362 * A087048 A109700 A087742

Adjacent sequences: A256119 A256120 A256121 * A256123 A256124 A256125

Keyword

nonn

Author

Michel Lagneau, Mar 15 2015

Status

approved