A036845 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.

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

Offset

1,3

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A096865(A000010(n)). - Antti Karttunen, Dec 06 2017

Example

The sequence {T(5,k)} is 4, 7, 6, 12, 4, 7, 6, 12,..., whose minimum value is 4. Hence a(5) = 4.

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 ] ] ]

Crossrefs

Cf. A000010, A000203, A036840, A066437, A096865.

Sequence in context: A054844 A057936 A033097 * A094269 A157227 A054536

Adjacent sequences: A036842 A036843 A036844 * A036846 A036847 A036848

Keyword

nonn,look

Author

Joseph L. Pe, Jan 09 2002

Extensions

Edited by Dean Hickerson, Jan 18 2002

Status

approved