login
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
OFFSET
1,2
COMMENTS
That is, before arriving at a number x such that A054973(x) > 1.
LINKS
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Apr 03 2015
STATUS
approved