cp's OEIS Frontend

A369638 The n-th arithmetic derivative of 2^7.

%I A369638 #8 Feb 05 2024 18:08:22
%S A369638 128,448,1408,5056,15232,56384,169216,677120,2902784,12008192,
%T A369638 49750016,323383296,2048106496,13312700416,79908855808,520115646464,
%U A369638 3120693882880,19851642843136,121321447460864,754017659596800,5330629212856320,37592273278603264,230970707522453504,1736195064174952448,12244744136813133824
%N A369638 The n-th arithmetic derivative of 2^7.
%C A369638 Iterates of the map k -> k', starting from k=128, where k' stands for the arithmetic derivative, A003415.
%H A369638 Antti Karttunen, <a href="/A369638/b369638.txt">Table of n, a(n) for n = 0..89</a>
%F A369638 a(0) = 128, and for n > 0, a(n) = A003415(a(n-1)).
%o A369638 (PARI)
%o A369638 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369638 A369638(n) = if(!n,128,A003415(A369638(n-1)));
%o A369638 (PARI)
%o A369638 up_to = 89;
%o A369638 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369638 A369638list(up_to) = { my(v=vector(up_to)); v[1] = 128;
%o A369638 for(i=2,up_to,print1(i,", "); v[i] = A003415(v[i-1])); (v); };
%o A369638 v369638 = A369638list(1+up_to);
%o A369638 A369638(n) = v369638[1+n];
%Y A369638 Row 128 of A258651.
%Y A369638 Cf. A003415, A369652 [= A328114(a(n))].
%Y A369638 Cf. also A001787, A129150.
%K A369638 nonn
%O A369638 0,1
%A A369638 _Antti Karttunen_, Feb 04 2024