A060605 a(n) = sum of lengths of the iteration sequences of Euler totient function from 1 to n.

1, 3, 6, 9, 13, 16, 20, 24, 28, 32, 37, 41, 46, 50, 55, 60, 66, 70, 75, 80, 85, 90, 96, 101, 107, 112, 117, 122, 128, 133, 139, 145, 151, 157, 163, 168, 174, 179, 185, 191, 198, 203, 209, 215, 221, 227, 234, 240, 246, 252, 259, 265, 272, 277, 284, 290, 296, 302

Offset: 1

Author

Labos Elemer, Apr 13 2001

Keywords

• nonn

Comments

Partial sums of A049108. - Joerg Arndt, Jan 06 2015

Examples

			Iteration sequences of Phi applied to 1, 2, 3, 4, 5, 6 give lengths 1, 2, 3, 3, 4, 3 with partial sums as follows:1, 3, 5, 9, 13, 16 resulting in first...6th terms here.
		

Links

• Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204.
• Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers]
• Harold Shapiro, An arithmetic function arising from the phi function, Amer. Math. Monthly, Vol. 50, No. 1 (1943), 18-30.

Crossrefs

Cf. A049108, A003434.

Programs

Mathematica

Accumulate[Table[Length[NestWhileList[EulerPhi,n,#!=1&]],{n,60}]] (* Harvey P. Dale, Mar 23 2024 *)

PARI

a049108(n)=my(t=1); while(n>1, t++; n=eulerphi(n)); t;
vector(80, n, sum(j=1, n, a049108(j))) \\ Michel Marcus, Jan 06 2015

Formula

a(n) = sum( j=1..n, A049108(j) ).