A019294 -id:A019294 - cp's OEIS frontend

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

Walter Nissen, Feb 18 2010

The last of these iterates is the value in A173430.

			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.

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.

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

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

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

A331035 a(n) = sigma^m(N)/N for N = A019276(n) (megaperfect numbers), where m(N) = min {m: N | sigma^m(N)} reaches record values; sigma^m is m-fold iteration of A000203.

Original entry on oeis.org

1, 2, 5, 24, 168, 1834560, 6516224, 881280, 517517500266693633076805172570524811961093324800, 12291248474277267848395134563637563923813851715476607482451722240, 9432427640268436606451425375305719340471711381221905226790680395776

Offset: 1

M. F. Hasler, Jan 08 2020

nonn

See A019294 for m as function of the starting value.

See the main sequence A019276 for further information and references.

Cf. A019276 (megaperfect numbers: where A019294 reaches records), A019277 (the record values), A019294 (min{m>0: n|sigma^m(n)}), A019295 (ratio sigma^m(n)/n).

a(n) = A019295(A019276(n)).

cp's OEIS Frontend

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

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