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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 (list; graph; refs; listen; history; text; internal format)
 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: A079487 A229122 A069010 * A087048 A109700 A087742 Adjacent sequences:  A256119 A256120 A256121 * A256123 A256124 A256125 KEYWORD nonn AUTHOR Michel Lagneau, Mar 15 2015 STATUS approved

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Last modified April 11 21:52 EDT 2021. Contains 342888 sequences. (Running on oeis4.)