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
Keywords
Examples
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.
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
Programs
-
Haskell
a053478 = (+ 1) . sum . takeWhile (/= 1) . iterate a000010 -- Reinhard Zumkeller, Oct 27 2011
-
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 *) -
PARI
a(n)=my(s=n);while(n>1,s+=n=eulerphi(n)); s \\ Charles R Greathouse IV, Feb 21 2013
Formula
a(n) = n + a(phi(n)).
a(n) = A092693(n) + n. - Vladeta Jovovic, Jul 02 2004
Comments