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A176846
Number of iterations of the map n-> n - sigma(bigomega(n)) needed to reach 1.
1
0, 1, 2, 1, 2, 3, 4, 2, 4, 5, 6, 3, 4, 7, 4, 5, 6, 8, 9, 6, 9, 10, 11, 7, 11, 12, 12, 8, 9, 13, 14, 13, 14, 15, 14, 10, 11, 15, 11, 15, 16, 16, 17, 16, 17, 18, 19, 17, 19, 19, 18, 18, 19, 20, 19, 20, 21, 20, 21, 20, 21, 22, 22, 19, 23, 23, 24, 20, 24, 24, 25, 24, 25, 26, 26, 25, 27
OFFSET
1,3
COMMENTS
The function n-A000203(A001222(n)) = 1, 1, 2, 1, 4, 3, 6, 4, 6, 7, 10, 8, 12,... (n>=1) is applied repeatedly starting at n.
The sequence counts the iterations needed to reach one of the 1.
LINKS
EXAMPLE
For n = 10, a(10) = 5 because 10 - sigma(bigomega(10)) = 7 (1st iter.);
7 - sigma(bigomega(7)) = 6 (2nd iter.); 6 - sigma(bigomega(6)) = 3 (3rd iter.);
3 - sigma(bigomega(3)) = 2 (4th iter.); 2 - sigma(bigomega(2)) = 1 (5th and last iter, reaching 1).
MAPLE
with(numtheory): n0:=200:tabl:=array(1..n0): for n from 1 to n0 do:k:=0:nn:=n: for q from 0 to 1000 while(nn<>1) do: nn:=nn - sigma(bigomega((nn))): k:=k+1: od: tabl[n]:=k: od: print(tabl):
MATHEMATICA
Table[Length[NestWhileList[#-DivisorSigma[1, PrimeOmega[#]]&, n, #!=1&]]-1, {n, 80}] (* Harvey P. Dale, Aug 08 2016 *)
CROSSREFS
Sequence in context: A033787 A165073 A369224 * A144735 A304734 A375088
KEYWORD
nonn,easy
AUTHOR
Michel Lagneau, Apr 27 2010
EXTENSIONS
Unspecific reference removed by R. J. Mathar, Oct 20 2010
STATUS
approved