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A363097
a(0) = 1, a(n) = n + phi(a(n-1)), where phi is Euler totient function.
0
1, 2, 3, 5, 8, 9, 12, 11, 18, 15, 18, 17, 28, 25, 34, 31, 46, 39, 42, 31, 50, 41, 62, 53, 76, 61, 86, 69, 72, 53, 82, 71, 102, 65, 82, 75, 76, 73, 110, 79, 118, 99, 102, 75, 84, 69, 90, 71, 118, 107, 156, 99, 112, 101, 154, 115, 144, 105, 106, 111, 132, 101, 162, 117, 136
OFFSET
0,2
COMMENTS
Conjecture: 1.25*n < a(n) < 4*n for n > 0.
EXAMPLE
a(5) = 9 because a(4) = 8 and 5 + phi(a(4)) = 5 + 4 = 9.
MAPLE
a:= proc(n) option remember;
`if`(n=0, 1, n+numtheory[phi](a(n-1)))
end:
seq(a(n), n=0..100); # Alois P. Heinz, May 20 2023
MATHEMATICA
a[0]=1; a[n_]:=a[n]=n+EulerPhi[a[n-1]]; Array[a, 65, 0]
CROSSREFS
Cf. A000010.
Sequence in context: A051214 A256722 A364926 * A192391 A013634 A133484
KEYWORD
nonn
AUTHOR
STATUS
approved