A176846 Number of iterations of the map n-> n - sigma(bigomega(n)) needed to reach 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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A000203, A001222.

Sequence in context: A033787 A165073 A369224 * A144735 A304734 A202275

Adjacent sequences: A176843 A176844 A176845 * A176847 A176848 A176849

Keyword

nonn,easy

Author

Michel Lagneau, Apr 27 2010

Extensions

Unspecific reference removed by R. J. Mathar, Oct 20 2010

Status

approved