This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A053478 #35 Aug 18 2024 20:19:50
%S A053478 1,3,6,7,12,9,16,15,18,17,28,19,32,23,30,31,48,27,46,35,40,39,62,39,
%T A053478 60,45,54,47,76,45,76,63,68,65,74,55,92,65,78,71,112,61,104,79,84,85,
%U A053478 132,79,110,85,114,91,144,81,126,95,112,105,164,91,152,107,118,127,144,101
%N A053478 Sum of iterates when phi, A000010, is iterated until fixed point 1.
%C A053478 For n = 2^w, the sum is 2^(w+1) - 1.
%H A053478 T. D. Noe, <a href="/A053478/b053478.txt">Table of n, a(n) for n = 1..10000</a>
%F A053478 a(n) = n + a(phi(n)).
%F A053478 a(n) = A092693(n) + n. - _Vladeta Jovovic_, Jul 02 2004
%e A053478 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.
%t A053478 f[n_] := Plus @@ Drop[ FixedPointList[ EulerPhi, n], -1]; Table[ f[n], {n, 66}] (* _Robert G. Wilson v_, Dec 16 2004 *)
%t A053478 f[1] := 1; f[n_] := n + f[EulerPhi[n]]; Table[f[n], {n, 66}] (* _Carlos Eduardo Olivieri_, May 26 2015 *)
%o A053478 (Haskell)
%o A053478 a053478 = (+ 1) . sum . takeWhile (/= 1) . iterate a000010
%o A053478 -- _Reinhard Zumkeller_, Oct 27 2011
%o A053478 (PARI) a(n)=my(s=n);while(n>1,s+=n=eulerphi(n)); s \\ _Charles R Greathouse IV_, Feb 21 2013
%Y A053478 Cf. A000010, A010554, A049099, A049100, A049107, A049108, A032358.
%Y A053478 Row sums of A375478.
%K A053478 nonn
%O A053478 1,2
%A A053478 _Labos Elemer_, Jan 14 2000