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

1, 15, 15, 15, 6, 6, 15, 15, 14, 10, 12, 12, 14, 14, 15, 104, 18, 18, 20, 20, 104, 22, 24, 24, 104, 26, 40, 28, 30, 30, 104, 104, 33, 34, 48, 91, 38, 38, 56, 40, 42, 42, 44, 44, 45, 46, 48, 48, 80, 255, 51, 52, 54, 54, 72, 56, 80, 58, 60, 60, 62, 62, 104, 255, 84, 66, 68, 68

Offset: 1

Author

Walter Nissen, Feb 18 2010

Keywords

• easy
• nonn

Examples

			Calculating sum-of-divisors ( ... sum-of-divisors ( sum-of-divisors ( 4 ) ) ... ) the iterates are 4, 7, 8, 15, 24, ... .
The initial, consecutive, pairwise, coprime iterates are 4, 7, 8, 15, so a(4) = 15 .
Here sigma ( 4 ) = 7, sigma ( sigma ( 4 ) ) = sigma ( 7 ) = 8, etc.
		

References

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, Vol. 5, No. 2 (1996), pp. 91-100.
• Leonard Eugene Dickson, History of the Theory of Numbers, Volume I, Divisibility and Primality, Carnegie Institution of Washington, 1919, Chapters II and X

Crossrefs

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

Programs

Mathematica

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 *)