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A173430 Last of consecutive coprime iterations of sum-of-divisors function 2

%I #11 Sep 02 2019 04:28:23

%S 1,15,15,15,6,6,15,15,14,10,12,12,14,14,15,104,18,18,20,20,104,22,24,

%T 24,104,26,40,28,30,30,104,104,33,34,48,91,38,38,56,40,42,42,44,44,45,

%U 46,48,48,80,255,51,52,54,54,72,56,80,58,60,60,62,62,104,255,84,66,68,68

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

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

%H Amiram Eldar, <a href="/A173430/b173430.txt">Table of n, a(n) for n = 1..10000</a>

%H Graeme L. Cohen and Herman J. J. te Riele, <a href="https://doi.org/10.1080/10586458.1996.10504580">Iterating the sum-of-divisors function</a>, Experimental Mathematics, Vol. 5, No. 2 (1996), pp. 91-100.

%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 ( 4 ) ) ... ) the iterates are 4, 7, 8, 15, 24, ... .

%e The initial, consecutive, pairwise, coprime iterates are 4, 7, 8, 15, so a(4) = 15 .

%e Here sigma ( 4 ) = 7, sigma ( sigma ( 4 ) ) = sigma ( 7 ) = 8, etc.

%t a[1] = 1; a[n_] := Module[{k = n}, While[CoprimeQ[k, (s = DivisorSigma[1, k])], k = s]; k]; Array[a, 68] (* _Amiram Eldar_, Sep 02 2019 *)

%Y Cf. 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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