cp's OEIS Frontend

A264970 If A262686(n) = 0, a(n) = 0, otherwise a(n) = 1 + a(A262686(n)), where A262686(n) = largest 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 A264970 #7 Dec 03 2015 04:36:07
%S A264970 12,2,11,2,1,1,10,0,0,3,2,2,9,0,1,5,1,4,8,0,0,3,7,2,0,0,2,1,0,1,6,6,1,
%T A264970 0,5,5,0,0,6,4,0,1,4,0,1,3,3,2,5,0,0,1,0,2,2,0,0,1,1,4,4,3,3,0,0,2,0,
%U A264970 0,0,1,2,3,3,2,0,0,2,1,4,0,1,1,3,3,2,0,2,2,0,4,3,1,1,3,2,5,1,4,0,2,0
%N A264970 If A262686(n) = 0, a(n) = 0, otherwise a(n) = 1 + a(A262686(n)), where A262686(n) = largest 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 A264970 a(n) = number of iterations of A262686 needed before zero is reached. In the context of tree (A263267) defined by edge-relation A049820(child) = parent, this is the number of hops we make before reaching one of the leaves (A045765), when we start from n and always select the largest child at each iteration.
%H A264970 Antti Karttunen, <a href="/A264970/b264970.txt">Table of n, a(n) for n = 0..10000</a>
%F A264970 If A060990(n) = 0, a(n) = 0, otherwise a(n) = 1 + a(A262686(n)).
%F A264970 Other identities. For all n >= 0:
%F A264970 a(n) = A264971(n) - 1.
%o A264970 (Scheme, with memoization-macro definec)
%o A264970 (definec (A264970 n) (cond ((A262686 n) => (lambda (lad) (if (zero? lad) 0 (+ 1 (A264970 lad)))))))
%Y A264970 Cf. A000005, A049820, A060990, A262686, A263267.
%Y A264970 Cf. A045765 (positions of zeros).
%Y A264970 One less than A264971.
%K A264970 nonn
%O A264970 0,1
%A A264970 _Antti Karttunen_, Nov 29 2015