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

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, 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, 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

Offset

1,2

Comments

The last of these iterates is the value in A173430.

References

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

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

Links

Table of n, a(n) for n=1..105.

Leonard Eugene Dickson, History of the Theory of Numbers, Volume I, Divisibility and Primality, Carnegie Institution of Washington, 1919, Chapters II and X

Example

Calculating sum-of-divisors ( ... sum-of-divisors ( sum-of-divisors ( 7 ) ) ... ) the iterates are 7, 8, 15, 24, ... .
The initial, consecutive, pairwise, coprime iterates are 7, 8, 15, and there are 3 of these, so a(7) = 3.
Here sigma ( 7 ) = 8, sigma ( sigma ( 7 ) ) = sigma ( 8 ) = 15, etc.

Prog

(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

Crossrefs

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

Sequence in context: A193178 A084448 A256596 * A263879 A085664 A154007

Adjacent sequences: A173428 A173429 A173430 * A173432 A173433 A173434

Keyword

easy,nonn

Author

Walter Nissen, Feb 18 2010

Status

approved