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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)).
4
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.
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 03 2015
STATUS
approved