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%I #14 Dec 06 2017 20:07:44
%S 1,1,2,2,4,2,4,4,4,4,4,4,12,4,8,8,16,4,16,8,12,4,12,8,12,12,16,12,16,
%T 8,16,16,12,16,16,12,36,16,16,16,16,12,32,12,16,12,16,16,32,12,32,16,
%U 32,16,16,16,36,16,16,16,48,16,36,32,48,12,48,32,16,16,48,16,72,36,16
%N a(n) = min_{k} {T(n,k)} where T(n,k) is the "phi/sigma tug-of-war sequence with seed n" defined by T(n,1) = phi(n), T(n,2) = sigma(phi(n)), T(n,3) = phi(sigma(phi(n))), ..., T(n,k) = phi(T(n,k-1)) if k is odd and = sigma(T(n,k-1)) if k is even.
%C Conjecture: The sequence {T(n,k)} is eventually periodic for every n, so a(n) can be computed in finite time.
%C Conjecture: a(n) -> infinity as n -> infinity.
%H Antti Karttunen, <a href="/A036845/b036845.txt">Table of n, a(n) for n = 1..16384</a>
%F a(n) = A096865(A000010(n)). - _Antti Karttunen_, Dec 06 2017
%e The sequence {T(5,k)} is 4, 7, 6, 12, 4, 7, 6, 12,..., whose minimum value is 4. Hence a(5) = 4.
%t a[ n_ ] := For[ m=EulerPhi[ n ]; min=Infinity; seq={m}, True, AppendTo[ seq, m ], If[ m<min, min=m ]; m=EulerPhi[ DivisorSigma[ 1, m ] ]; If[ MemberQ[ seq, m ], Return[ min ] ] ]
%Y Cf. A000010, A000203, A036840, A066437, A096865.
%K nonn,look
%O 1,3
%A _Joseph L. Pe_, Jan 09 2002
%E Edited by _Dean Hickerson_, Jan 18 2002
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