A266111 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).

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, 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, 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

Offset

0,1

Links

Antti Karttunen, Table of n, a(n) for n = 0..10000

Formula

If A060990(n) = 0, a(n) = 1, otherwise a(n) = 1 + a(A082284(n)).

Other identities. For all n >= 0:

a(n) = 1 + A266110(n).

Example

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.

Prog

(Scheme, with memoization-macro definec)
(definec (A266111 n) (cond ((A082284 n) => (lambda (lad) (if (zero? lad) 1 (+ 1 (A266111 lad)))))))

Crossrefs

One more than A266110.

Number of significant terms on row n of A265751 (without its trailing zeros).

Cf. tree A263267 (and its illustration).

Cf. A000005, A060990, A082284.

Cf. also A264971.

Sequence in context: A018840 A058209 A160789 * A131291 A305394 A361803

Adjacent sequences: A266108 A266109 A266110 * A266112 A266113 A266114

Keyword

nonn

Author

Antti Karttunen, Dec 21 2015

Status

approved