cp's OEIS Frontend

A090637 Trajectory of 28 under the map k -> A003415(k) (taking the arithmetic derivative).

%I A090637 #26 Jan 13 2025 06:24:18
%S A090637 28,32,80,176,368,752,1520,3424,8592,20096,70464,235072,705280,
%T A090637 3023616,13223680,55540736,278539264,1392697344,9541095424,
%U A090637 58609614848,410267320320,3397142953984,24143851798528,176071227916288,1232666139967488,9523075842834432
%N A090637 Trajectory of 28 under the map k -> A003415(k) (taking the arithmetic derivative).
%C A090637 Equals A090636 from a(2) = 32 = A090636(5) on. See there and A090635 for more.
%H A090637 Alois P. Heinz, <a href="/A090637/b090637.txt">Table of n, a(n) for n = 1..100</a>
%e A090637 a(2) = 28' = (2^2*7)' = 28*(2/2 + 1/7) = 32.
%p A090637 a:= proc(n) option remember; `if`(n=1, 28, (t->
%p A090637       t*add(i[2]/i[1], i=ifactors(t)[2]))(a(n-1)))
%p A090637     end:
%p A090637 seq(a(n), n=1..31);  # _Alois P. Heinz_, Dec 02 2019
%t A090637 a[n_] := a[n] = If[n == 1, 28, Function[t, t*Sum[i[[2]]/i[[1]], {i, FactorInteger[t]}]][a[n-1]]];Table[a[n], {n, 1, 31}] (* _Jean-François Alcover_, Jan 13 2025, after _Alois P. Heinz_ *)
%o A090637 (PARI) a(n)=A090636(n,28)
%Y A090637 Cf. A090636, A090635.
%K A090637 nonn
%O A090637 1,1
%A A090637 _N. J. A. Sloane_, Dec 14 2003
%E A090637 Edited by _M. F. Hasler_, Nov 27 2019