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

128, 448, 1408, 5056, 15232, 56384, 169216, 677120, 2902784, 12008192, 49750016, 323383296, 2048106496, 13312700416, 79908855808, 520115646464, 3120693882880, 19851642843136, 121321447460864, 754017659596800, 5330629212856320, 37592273278603264, 230970707522453504, 1736195064174952448, 12244744136813133824

Offset: 0

Author

Antti Karttunen, Feb 04 2024

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 0..89

Crossrefs

Row 128 of A258651.

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

Cf. also A001787, A129150.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369638(n) = if(!n,128,A003415(A369638(n-1)));

PARI

up_to = 89;
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369638list(up_to) = { my(v=vector(up_to)); v[1] = 128;
for(i=2,up_to,print1(i,", "); v[i] = A003415(v[i-1])); (v); };
v369638 = A369638list(1+up_to);
A369638(n) = v369638[1+n];

Formula

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