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 A173431 Count of consecutive coprime iterations of sum-of-divisors function 0

%I

%S 1,6,5,4,2,1,3,2,3,1,2,1,2,1,1,5,2,1,2,1,4,1,2,1,5,1,2,1,2,1,4,3,1,1,

%T 2,2,2,1,2,1,2,1,2,1,1,1,2,1,3,4,1,1,2,1,2,1,2,1,2,1,2,1,2,4,2,1,2,1,

%U 1,1,2,1,2,1,2,1,2,1,2,1,4,1,2,1,2,1,1,1,2,1,1,1,3,1,1,1,4,3,1,5,2,1,2,1,1

%N Count of consecutive coprime iterations of sum-of-divisors function

%C The last of these iterates is the value in A173430.

%D Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

%D Oystein Ore, Number Theory and Its History, 1988, Dover Publications, ISBN 0486656209, pp. 88-96.

%H Leonard Eugene Dickson, History of the Theory of Numbers, <a href="http://books.google.com/books?id=mbk9AAAAYAAJ">Volume I</a>, Divisibility and Primality, Carnegie Institution of Washington, 1919, Chapters II and X

%e Calculating sum-of-divisors ( ... sum-of-divisors ( sum-of-divisors ( 7 ) ) ... ) the iterates are 7, 8, 15, 24, ... .

%e The initial, consecutive, pairwise, coprime iterates are 7, 8, 15, and there are 3 of these, so a(7) = 3.

%e Here sigma ( 7 ) = 8, sigma ( sigma ( 7 ) ) = sigma ( 8 ) = 15, etc.

%o (PARI) a(n)=my(t,s);if(n==1,1,while(1,s++;t=sigma(n);if(gcd(t,n)==1,n=t,return(s)))) \\ _Charles R Greathouse IV_, Feb 06 2012

%Y Cf. A173430, A129246 and the references there, A019294, A019295, A000203, A051027, A019284, A019277.

%K easy,nonn

%O 1,2

%A _Walter Nissen_, Feb 18 2010

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Last modified September 20 07:46 EDT 2020. Contains 337264 sequences. (Running on oeis4.)