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A256596 a(n) is the number of iterations of the map x->sigma(x) when starting from n before arriving at a number with more than one ancestor, with a(1)=0 and where sigma is the sum of divisors. 0
0, 6, 5, 4, 2, 1, 3, 2, 3, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 4, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

That is, before arriving at a number x such that A054973(x) > 1.

LINKS

Table of n, a(n) for n=1..88.

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

EXAMPLE

For n=2, the repeated map gives 2 -> 3 -> 4 -> 7 -> 8 -> 15 -> 24 where 24 is the first fork with sigma(15)=sigma(23)=24, so with 6 iterations starting from 2 we have a(2)=6, a(3)=5, a(4)=4, a(7)=3, a(8)=2, and a(15)=1.

PROG

(PARI) isfork(n) = {my(nba = 0); for (i=2, n-1, if (sigma(i) == n, nba++); if (nba > 1, return (1)); ); }

a(n) = {if (n==1, return (0)); my(nbit = 0); ok = 0; while (! ok, newn = sigma(n); nbit++; ok = isfork(newn); n = newn; ); nbit; }

CROSSREFS

Cf. A000203, A054973, A085790, A216200, A241954.

Sequence in context: A110390 A193178 A084448 * A173431 A263879 A085664

Adjacent sequences:  A256593 A256594 A256595 * A256597 A256598 A256599

KEYWORD

nonn

AUTHOR

Michel Marcus, Apr 03 2015

STATUS

approved

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Last modified September 20 17:16 EDT 2020. Contains 337265 sequences. (Running on oeis4.)