OFFSET
1,3
COMMENTS
Conjecture: a(n) is always finite; i.e. the sequence {T(n,k)} is eventually periodic for every n.
a(n) >= sigma(phi(n)) >= phi(n); since phi(n) -> infinity with n, so does a(n).
Sequence is otherwise like A096864, except here the initial value n where the iteration is started from is ignored. - Antti Karttunen, Dec 06 2017
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
FORMULA
EXAMPLE
For n=11, the sequence is 11, 10, 18, 6, 12, 4, 7, 6, 12, ..., whose maximum value is 18. Hence a(11) = 18.
MATHEMATICA
a[ n_ ] := For[ m=n; max=0; seq={}, True, AppendTo[ seq, m ], If[ (m=DivisorSigma[ 1, EulerPhi[ m ] ])>max, max=m ]; If[ MemberQ[ seq, m ], Return[ max ] ] ]
PROG
(Scheme) (define (A066437 n) (let loop ((visited (list n)) (i 1) (m 1)) (let ((next ((if (odd? i) A000010 A000203) (car visited)))) (cond ((member next (reverse visited)) => (lambda (start_of_cyclic_part) (cond ((even? (length start_of_cyclic_part)) (max m next)) (else (loop (cons next visited) (+ 1 i) (max m next)))))) (else (loop (cons next visited) (+ 1 i) (max m next))))))) ;; Antti Karttunen, Dec 06 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Jan 08 2002
EXTENSIONS
Edited by Dean Hickerson, Jan 18 2002
STATUS
approved