A262676 Number of nonzero even numbers encountered when iterating A049820 starting from n: a(0) = 0 and for n >= 1, a(n) = (1-A000035(n)) + a(A049820(n)).

0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 3, 2, 3, 2, 4, 2, 3, 2, 4, 2, 5, 2, 5, 2, 4, 5, 6, 2, 6, 2, 6, 2, 7, 2, 7, 2, 3, 2, 8, 2, 8, 2, 8, 2, 9, 2, 9, 2, 9, 9, 10, 2, 10, 2, 10, 2, 10, 2, 11, 2, 10, 2, 12, 2, 3, 2, 12, 2, 13, 2, 13, 2, 11, 2, 14, 2, 14, 2, 14, 2, 14, 14, 15, 14, 12, 14, 16, 14, 15, 14, 15, 14, 17, 14, 16, 14, 13, 14, 18, 14, 15, 14, 17

Offset

0,7

Comments

Number of even numbers encountered before zero is reached when starting from k = n and repeatedly applying the map that replaces k by k - d(k), where d(k) is the number of divisors of k (A000005). This count includes n itself if it is even, but excludes the zero.

Links

Antti Karttunen, Table of n, a(n) for n = 0..10080

A. Karttunen, Ratio a(n)/A262677(n) drawn with the help of OEIS Plot2-script

Formula

a(0) = 0; for n >= 1, a(n) = (1-A000035(n)) + a(A049820(n)).

Other identities. For all n >= 0:

A155043(n) = a(n) + A262677(n).

Prog

(Scheme, with memoization-macro definec)
(definec (A262676 n) (if (zero? n) n (+ (- 1 (A000035 n)) (A262676 (A049820 n)))))

Crossrefs

Cf. A000005, A000035, A049820, A155043, A262677, A262680.

Sequence in context: A164733 A288311 A244366 * A070101 A022830 A035663

Adjacent sequences: A262673 A262674 A262675 * A262677 A262678 A262679

Keyword

nonn

Author

Antti Karttunen, Oct 03 2015

Status

approved