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%I #13 Jun 03 2018 02:02:53
%S 5,4,5,3,2,2,4,1,1,3,3,2,4,1,2,3,2,2,3,1,1,7,2,6,1,1,3,5,1,4,5,3,2,1,
%T 4,2,1,1,3,3,1,2,3,1,2,9,2,8,2,1,1,7,1,6,4,1,1,5,3,4,8,3,2,1,1,2,1,1,
%U 1,5,2,4,7,3,1,1,9,2,5,1,2,8,4,7,6,1,3,6,1,5,13,6,2,4,12,5,5,4,1,3,1,2,11,1,4,3,10,2,1,1,2,2,1,1,9,3,1,1,8,2,3,7
%N If A082284(n) = 0, a(n) = 1, otherwise a(n) = 1 + a(A082284(n)), where A082284(n) = smallest number k such that k - d(k) = n, or 0 if no such number exists, and d(n) = the number of divisors of n (A000005).
%H Antti Karttunen, <a href="/A266111/b266111.txt">Table of n, a(n) for n = 0..10000</a>
%F If A060990(n) = 0, a(n) = 1, otherwise a(n) = 1 + a(A082284(n)).
%F Other identities. For all n >= 0:
%F a(n) = 1 + A266110(n).
%e Starting from n = 21, we get the following chain: 21 -> 23 -> 27 -> 29 -> 31 -> 35 -> 37, with A082284 iterated 6 times before the final term 37 (for which A060990(37) = A082284(37) = 0) is encountered. Here we count the terms (not steps) in whole chain, thus a(21) = 7.
%o (Scheme, with memoization-macro definec)
%o (definec (A266111 n) (cond ((A082284 n) => (lambda (lad) (if (zero? lad) 1 (+ 1 (A266111 lad)))))))
%Y One more than A266110.
%Y Number of significant terms on row n of A265751 (without its trailing zeros).
%Y Cf. tree A263267 (and its illustration).
%Y Cf. A000005, A060990, A082284.
%Y Cf. also A264971.
%K nonn
%O 0,1
%A _Antti Karttunen_, Dec 21 2015
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