This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A082878 #13 Mar 25 2025 20:08:14
%S A082878 5,7,16,9,8,21,24,10,13,44,15,32,14,19,12,21,16,68,48,39,25,112,45,20,
%T A082878 56,81,16,92,22,31,33,51,18,72,26,39,55,80,18,176,43,22,45,32,140,20,
%U A082878 96,34,49,24,272,77,75,164,55,40,240,28,120,87,61,24,63,44,128,46,26,69
%N A082878 Arithmetic derivative of numbers of the form p*q^k with distinct primes p and q, k > 0.
%H A082878 Amiram Eldar, <a href="/A082878/b082878.txt">Table of n, a(n) for n = 1..10000</a>
%F A082878 a(n) = A003415(A084227(n)).
%F A082878 a(p*q^k) = (p+q)*q^(k-1).
%t A082878 s[n_] := Module[{f = FactorInteger[n], i}, If[Length[f] == 2 && Min[f[[;;, 2]]] == 1, i = FirstPosition[f[[;;, 2]], 1][[1]]; n * (1/f[[i, 1]] + f[[3-i, 2]] /f[[3-i, 1]]), Nothing]]; Array[s, 100] (* _Amiram Eldar_, Mar 25 2025 *)
%Y A082878 Cf. A003415, A084227.
%K A082878 nonn
%O A082878 1,1
%A A082878 _Reinhard Zumkeller_, May 25 2003
%E A082878 Data corrected by _Amiram Eldar_, Mar 25 2025