%I #10 Mar 01 2021 17:55:14

%S 1,1,2,1,1,1,2,1,1,1,8,1,3,4,16,1,1,1,4,1,1,1,2,1,1,9,16,1,1,1,8,1,1,

%T 2,2,1,1,8,2,1,1,1,8,1,5,1,8,1,3,2,4,1,27,8,2,1,1,1,2,1,1,1,32,3,1,1,

%U 12,1,1,1,2,1,1,1,8,3,1,1,8,18,1,1,2,1,3,16,2,1,1,2,16,1,7,4,8,1,1,5,2,1,1,1,2,1

%N Arithmetic derivative of n divided by its largest squarefree divisor: a(n) = A003557(A003415(n)).

%H Antti Karttunen, <a href="/A341998/b341998.txt">Table of n, a(n) for n = 2..16384</a>

%H Antti Karttunen, <a href="/A341998/a341998.txt">Data supplement: n, a(n) computed for n = 2..65539</a>

%F a(n) = A003557(A003415(n)).

%o (PARI)

%o A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415

%o A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557

%o A341998(n) = if(n<=1,1,A003557(A003415(n)));

%Y Cf. A003415, A003557, A341994, A341997, A342001.

%Y Cf. A328393 (positions of ones), A328303 (after its two initial terms, gives the positions of terms > 1).

%K nonn

%O 2,3

%A _Antti Karttunen_, Feb 28 2021