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Trajectory of 28 under the map k -> A003415(k) (taking the arithmetic derivative).
3

%I #20 Dec 03 2019 07:15:01

%S 28,32,80,176,368,752,1520,3424,8592,20096,70464,235072,705280,

%T 3023616,13223680,55540736,278539264,1392697344,9541095424,

%U 58609614848,410267320320,3397142953984,24143851798528,176071227916288,1232666139967488,9523075842834432

%N Trajectory of 28 under the map k -> A003415(k) (taking the arithmetic derivative).

%C Equals A090636 from a(2) = 32 = A090636(5) on. See there and A090635 for more.

%H Alois P. Heinz, <a href="/A090637/b090637.txt">Table of n, a(n) for n = 1..100</a>

%e a(2) = 28' = (2^2*7)' = 28*(2/2 + 1/7) = 32.

%p a:= proc(n) option remember; `if`(n=1, 28, (t->

%p t*add(i[2]/i[1], i=ifactors(t)[2]))(a(n-1)))

%p end:

%p seq(a(n), n=1..31); # _Alois P. Heinz_, Dec 02 2019

%o (PARI) a(n)=A090636(n,28)

%Y Cf. A090636, A090635.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 14 2003

%E Edited by _M. F. Hasler_, Nov 27 2019