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A053470
a(n) is the cototient of n (A051953) iterated twice.
4
0, 0, 0, 1, 0, 2, 0, 2, 1, 4, 0, 4, 0, 4, 1, 4, 0, 8, 0, 8, 3, 8, 0, 8, 1, 8, 3, 8, 0, 12, 0, 8, 1, 12, 1, 16, 0, 12, 7, 16, 0, 22, 0, 16, 9, 16, 0, 16, 1, 22, 1, 16, 0, 24, 7, 16, 9, 22, 0, 24, 0, 16, 9, 16, 1, 24, 0, 24, 5, 24, 0, 32, 0, 20, 11, 24, 1, 36, 0, 32, 9, 30, 0, 44, 9, 24, 1, 32, 0
OFFSET
1,6
COMMENTS
Iteration of A051953 is ended at fixed point 0. Analogous 2nd iterates for number of divisors (A000005) and Euler-Phi (A000010) are A036454 and A010554.
LINKS
FORMULA
a(1) = 0; for n > 1, a(n) = A051953(A051953(n)).
EXAMPLE
n=50, n_1 = n - phi(n) = 50 - 20 = 30, n_2 = n_1 - Phi(n_1) = 30 - 8 = 22, so the 50th term is 22.
MATHEMATICA
Array[Nest[# - EulerPhi@ # &, #, 2] &, 89] (* Michael De Vlieger, Dec 23 2017 *)
PROG
(PARI)
A051953(n) = (n-eulerphi(n));
A053470(n) = if(1==n, 0, A051953(A051953(n))); \\ Antti Karttunen, Dec 22 2017
KEYWORD
nonn
AUTHOR
Labos Elemer, Jan 14 2000
STATUS
approved