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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).
1
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
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Mar 15 2015
STATUS
approved