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A291934
Largest k achievable by the iteration k->(sigma(k)+phi(k))/2 started at k=n, with termination when sigma(k) becomes odd.
2
1, 2, 3, 4, 5, 7, 7, 8, 9, 11, 11, 16, 13, 16, 16, 16, 17, 18, 19, 25, 23, 23, 23, 36, 25, 29, 29, 36, 29, 53, 31, 32, 36, 36, 36, 36, 37, 53, 53, 53, 41, 144, 43, 61, 61, 47, 47, 144, 49, 50, 61, 61, 53, 144, 72, 72, 59, 59, 59, 107, 61, 144
OFFSET
1,2
COMMENTS
See A291914 for types of termination. The first term with unknown conjecturally unbounded behavior is a(270). More values of n with this type of behavior are given in A291790.
All bounded terms of this sequence are either prime or in A028982.
LINKS
EXAMPLE
a(38)=53: Starting with k=38 produces the trajectory 38 -> 39 -> 50 -> 53 -> 53 ...
a(42)=144: See example in A290001.
MATHEMATICA
With[{lim = 100}, TakeWhile[#, # > 0 &] &@ Table[Which[Length@ # < lim, Last@ #, SameQ @@ Take[#, -2], Last@ #, True, 0] &@ NestWhileList[(DivisorSigma[1, #] + EulerPhi[#])/2 &, n, EvenQ@ DivisorSigma[1, #] &, 1, lim], {n, 270}]] (* Michael De Vlieger, Sep 06 2017 *)
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Sep 06 2017
STATUS
approved