A369638 - OEIS

%I #8 Feb 05 2024 18:08:22

%S 128,448,1408,5056,15232,56384,169216,677120,2902784,12008192,

%T 49750016,323383296,2048106496,13312700416,79908855808,520115646464,

%U 3120693882880,19851642843136,121321447460864,754017659596800,5330629212856320,37592273278603264,230970707522453504,1736195064174952448,12244744136813133824

%N The n-th arithmetic derivative of 2^7.

%C Iterates of the map k -> k', starting from k=128, where k' stands for the arithmetic derivative, A003415.

%H Antti Karttunen, <a href="/A369638/b369638.txt">Table of n, a(n) for n = 0..89</a>

%F a(0) = 128, and for n > 0, a(n) = A003415(a(n-1)).

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A369638(n) = if(!n,128,A003415(A369638(n-1)));

%o (PARI)

%o up_to = 89;

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A369638list(up_to) = { my(v=vector(up_to)); v[1] = 128;

%o for(i=2,up_to,print1(i,", "); v[i] = A003415(v[i-1])); (v); };

%o v369638 = A369638list(1+up_to);

%o A369638(n) = v369638[1+n];

%Y Row 128 of A258651.

%Y Cf. A003415, A369652 [= A328114(a(n))].

%Y Cf. also A001787, A129150.

%K nonn

%O 0,1

%A _Antti Karttunen_, Feb 04 2024