cp's OEIS Frontend

A266110 If A082284(n) = 0, a(n) = 0, 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).

%I A266110 #12 Nov 21 2018 00:33:05
%S A266110 4,3,4,2,1,1,3,0,0,2,2,1,3,0,1,2,1,1,2,0,0,6,1,5,0,0,2,4,0,3,4,2,1,0,
%T A266110 3,1,0,0,2,2,0,1,2,0,1,8,1,7,1,0,0,6,0,5,3,0,0,4,2,3,7,2,1,0,0,1,0,0,
%U A266110 0,4,1,3,6,2,0,0,8,1,4,0,1,7,3,6,5,0,2,5,0,4,12,5,1,3,11,4,4,3,0,2,0,1,10,0,3,2,9,1,0,0,1,1,0,0,8,2,0,0,7,1,2,6
%N A266110 If A082284(n) = 0, a(n) = 0, 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).
%C A266110 Starting from n, search for a smallest number k such that k - d(k) = n, and if found such a number, replace n with k and repeat the procedure. When eventually such k is no longer found, then (new) n must be one of the terms of A045765. The number of times the procedure can be repeated before that happens is the value of a(n). Sequence A266116 gives the stopping value of n.
%H A266110 Antti Karttunen, <a href="/A266110/b266110.txt">Table of n, a(n) for n = 0..124340</a>
%e A266110 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) = 6.
%o A266110 (Scheme, with memoization-macro definec)
%o A266110 (definec (A266110 n) (cond ((A082284 n) => (lambda (lad) (if (zero? lad) 0 (+ 1 (A266110 lad)))))))
%Y A266110 One less than A266111.
%Y A266110 Cf. A000005, A060990, A082284, A266116.
%Y A266110 Cf. A045765 (positions of zeros).
%Y A266110 Cf. tree A263267 (and its illustration).
%Y A266110 Cf. also A264970.
%K A266110 nonn
%O A266110 0,1
%A A266110 _Antti Karttunen_, Dec 21 2015