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A176842
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The number of iterations of the map x -> x - phi(bigomega(x)) needed to reach 1 starting at x=n.
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1
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0, 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 28, 29, 29, 30, 31, 32, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 42, 43, 43, 44, 43, 44
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OFFSET
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1,3
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COMMENTS
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bigomega is A001222, and phi is the Euler totient function A000010.
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LINKS
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Table of n, a(n) for n=1..73.
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EXAMPLE
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Starting with n = 6, a(6)=5 iterations are needed because :
f(6) = 6 - phi(bigomega(6)) = 6 - phi(2) = 6 - 1 = 5;
f(5) = 5 - phi(bigomega(5)) = 5 - phi(1) = 5 - 1 = 4;
f(4) = 4 - phi(bigomega(4)) = 4 - phi(2) = 4 - 1 = 3;
f(3) = 3 - phi(bigomega(3)) = 3 - phi(1) = 3 - 1 = 2 ;
f(2) = 2 - phi(bigomega(2)) = 2 - phi(1) = 2 - 1 = 1, and a(6) = 5.
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MAPLE
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A176842 := proc(n) local it, nmap ; it := 0 ; nmap := n ; while nmap <> 1 do nmap := nmap-numtheory[phi](numtheory[bigomega](nmap)) ; it := it+1 ; end do: it ; end proc: # R. J. Mathar, Jun 01 2011
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CROSSREFS
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Sequence in context: A121604 A071520 A195918 * A099848 A082287 A210062
Adjacent sequences: A176839 A176840 A176841 * A176843 A176844 A176845
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KEYWORD
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nonn,easy
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AUTHOR
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Michel Lagneau, Apr 27 2010
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STATUS
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approved
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