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A036845
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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.
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2
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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, 8, 16, 16, 12, 16, 16, 12, 36, 16, 16, 16, 16, 12, 32, 12, 16, 12, 16, 16, 32, 12, 32, 16, 32, 16, 16, 16, 36, 16, 16, 16, 48, 16, 36, 32, 48, 12, 48, 32, 16, 16, 48, 16, 72, 36, 16
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Conjecture: The sequence {T(n,k)} is eventually periodic for every n, so a(n) can be computed in finite time.
Conjecture: a(n) -> infinity as n -> infinity.
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EXAMPLE
| The sequence {T(5,k)} is 4, 7, 6, 12, 4, 7, 6, 12,..., whose minimum value is 4. Hence a(5) = 4.
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MATHEMATICA
| 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 ] ] ]
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CROSSREFS
| Cf. A000010, A000203, A036840, A066437.
Sequence in context: A054844 A057936 A033097 * A094269 A157227 A054536
Adjacent sequences: A036842 A036843 A036844 * A036846 A036847 A036848
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KEYWORD
| nonn
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 09 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 18 2002
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