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%I #20 Nov 20 2018 05:20:43
%S 7,7,13,7,8,7,13,7,8,13,20,13,25,13,20,19,24,19,25,19,20,37,25,37,24,
%T 25,40,37,28,37,50,37,40,33,50,37,36,37,50,43,40,43,49,43,50,67,49,67,
%U 56,49,50,67,52,67,68,55,56,67,68,67,136,67,68,63,64,67,66,67,68,79,74,79,136,79,74,75,103,79,98,79,88,103,98,103,136,85
%N The last nonzero term on each row of A265751.
%C Starting from j = n, search for a smallest number k such that k - d(k) = j, and if found such a number, replace j with k and repeat the procedure. When eventually such k is no longer found, then the (last such) j must be one of the terms of A045765, and it is set as the value of a(n).
%H Antti Karttunen, <a href="/A266116/b266116.txt">Table of n, a(n) for n = 0..124340</a>
%F a(n) = A265751(n, A266110(n)).
%F If A060990(n) = 0, a(n) = n, otherwise a(n) = 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).
%F Other identities and observations. For all n >= 0:
%F a(n) >= n.
%F A060990(a(n)) = 0. [All terms are in A045765.]
%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. Thus a(21) = 37.
%o (Scheme)
%o (definec (A266116 n) (cond ((A082284 n) => (lambda (lad) (if (zero? lad) n (A266116 lad))))))
%o ;; Alternatively:
%o (define (A266116 n) (A265751bi n (A266110 n))) ;; Code for A265751bi given in A265751.
%Y Cf. A000005, A045765, A060990, A082284, A265751.
%Y Cf. A266110 (gives the number of iterations of A082284 needed before a(n) is found).
%Y Cf. also tree A263267 (and its illustration).
%K nonn
%O 0,1
%A _Antti Karttunen_, Dec 21 2015
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