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A173431 Count of consecutive coprime iterations of sum-of-divisors function 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 14 06:43 EDT 2020. Contains 336477 sequences. (Running on oeis4.)