|
Search: id:A036845
|
|
|
| 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. |
|
+0
3
|
|
| 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; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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.
|
|
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.
Sequence in context: A054844 A057936 A033097 this_sequence A094269 A054536 A001316
Adjacent sequences: A036842 A036843 A036844 this_sequence A036846 A036847 A036848
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 09 2002
|
|
EXTENSIONS
|
Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Jan 18 2002
|
|
|
Search completed in 0.002 seconds
|
