A262677 - OEIS

A262677

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

0, 1, 0, 2, 1, 3, 0, 4, 1, 1, 0, 2, 0, 3, 0, 3, 2, 4, 0, 5, 0, 5, 0, 6, 2, 1, 0, 7, 0, 8, 0, 9, 0, 9, 0, 10, 7, 11, 0, 11, 0, 12, 0, 13, 0, 12, 0, 13, 0, 1, 0, 14, 0, 15, 0, 15, 0, 16, 0, 17, 0, 18, 0, 17, 16, 19, 0, 20, 0, 20, 0, 21, 0, 22, 0, 21, 0, 23, 0, 24, 0, 1, 0, 2, 0, 2, 0, 3, 0, 4, 0, 4, 0, 5, 0, 5, 0, 6, 0, 6, 4, 7, 0, 8, 0, 7, 0, 8

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

Number of odd 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 odd.

LINKS

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

FORMULA

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

Other identities. For all n >= 0:

A155043(n) = A262676(n) + a(n).

PROG

(Scheme, with memoization-macro definec)

(definec (A262677 n) (if (zero? n) n (+ (A000035 n) (A262677 (A049820 n)))))

CROSSREFS

Cf. A000005, A000035, A049820, A155043, A262676, A262680.

Sequence in context: A357991 A096269 A260437 * A307742 A297109 A073312

Adjacent sequences: A262674 A262675 A262676 * A262678 A262679 A262680

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 03 2015

STATUS

approved