A053478 Sum of iterates when phi, A000010, is iterated until fixed point 1.

1, 3, 6, 7, 12, 9, 16, 15, 18, 17, 28, 19, 32, 23, 30, 31, 48, 27, 46, 35, 40, 39, 62, 39, 60, 45, 54, 47, 76, 45, 76, 63, 68, 65, 74, 55, 92, 65, 78, 71, 112, 61, 104, 79, 84, 85, 132, 79, 110, 85, 114, 91, 144, 81, 126, 95, 112, 105, 164, 91, 152, 107, 118, 127, 144, 101

Offset

1,2

Comments

For n = 2^w, the sum is 2^(w+1) - 1.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

a(n) = n + a(phi(n)).

a(n) = A092693(n) + n. - Vladeta Jovovic, Jul 02 2004

Example

If phi is applied repeatedly to n = 91, the iterates {91, 72, 24, 8, 4, 2, 1} are obtained. Their sum is a(91) = 91 + 72 + 24 + 8 + 4 + 2 + 1 = 202.

Mathematica

f[n_] := Plus @@ Drop[ FixedPointList[ EulerPhi, n], -1]; Table[ f[n], {n, 66}] (* Robert G. Wilson v, Dec 16 2004 *)
f[1] := 1; f[n_] := n + f[EulerPhi[n]]; Table[f[n], {n, 66}] (* Carlos Eduardo Olivieri, May 26 2015 *)

Prog

(Haskell)
a053478 = (+ 1) . sum . takeWhile (/= 1) . iterate a000010
-- Reinhard Zumkeller, Oct 27 2011
(PARI) a(n)=my(s=n); while(n>1, s+=n=eulerphi(n)); s \\ Charles R Greathouse IV, Feb 21 2013

Crossrefs

Cf. A000010, A010554, A049099, A049100, A049107, A049108, A032358.

Sequence in context: A298794 A181683 A084125 * A269363 A138037 A209246

Adjacent sequences: A053475 A053476 A053477 * A053479 A053480 A053481

Keyword

nonn

Author

Labos Elemer, Jan 14 2000

Status

approved