%I #31 Feb 22 2018 16:42:57
%S 4,1,7,1,32,1,13,10,32,1,19,1,68,1,25,14,56,16,31,1,192,1,59,1,80,1,
%T 43,22,140,20,49,1,140,1,55,1,240,28,61,22,128,1,101,26,212,1,73,34,
%U 152,1,113,1,432,1,85,26,176,95,91,1,284,28,143,1,252,1,103
%N Arithmetic derivative of (3*n + 1), n >= 1, (A016777)'.
%C Comparing A016777(n) = 3n+1 and its arithmetic derivative a(n) = (A016777(n))' allows us to select the primes in A016777, because (prime(n))' = 1.
%H Freimut Marschner, <a href="/A245838/b245838.txt">Table of n, a(n) for n = 1..100000</a>
%F a(n) = (3*n + 1)' = (A016777(n))' = A003415(A016777(n)).
%e a(2) = (3*2 + 1)' = (7)' = 1, a(5846) = (A016777(5846))' = (3*5846 + 1)' = (17539)' = 1.
%p ad:= n -> n*add(f[2]/f[1], f=ifactors(n)[2]):
%p seq(ad(3*n+1), n=1..100); # _Robert Israel_, Aug 25 2014
%o (PARI) a(n) = my(n=3*n+1);sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i]); \\ _Michel Marcus_, Aug 12 2014
%Y Cf. A003415 (arithmetic derivative), A016777 (3n+1), A002476 (Primes of form 6m + 1).
%K nonn
%O 1,1
%A _Freimut Marschner_, Aug 06 2014
%E Edited: in name n>=0 replaced by n>=1. Example corrected. - _Wolfdieter Lang_, Oct 14 2014
%E Missing comma in data at a(63) inserted by _Andrew Howroyd_, Feb 22 2018