cp's OEIS Frontend

A341998 Arithmetic derivative of n divided by its largest squarefree divisor: a(n) = A003557(A003415(n)).

%I A341998 #10 Mar 01 2021 17:55:14
%S A341998 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 A341998 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 A341998 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 A341998 Arithmetic derivative of n divided by its largest squarefree divisor: a(n) = A003557(A003415(n)).
%H A341998 Antti Karttunen, <a href="/A341998/b341998.txt">Table of n, a(n) for n = 2..16384</a>
%H A341998 Antti Karttunen, <a href="/A341998/a341998.txt">Data supplement: n, a(n) computed for n = 2..65539</a>
%F A341998 a(n) = A003557(A003415(n)).
%o A341998 (PARI)
%o A341998 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 A341998 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
%o A341998 A341998(n) = if(n<=1,1,A003557(A003415(n)));
%Y A341998 Cf. A003415, A003557, A341994, A341997, A342001.
%Y A341998 Cf. A328393 (positions of ones), A328303 (after its two initial terms, gives the positions of terms > 1).
%K A341998 nonn
%O A341998 2,3
%A A341998 _Antti Karttunen_, Feb 28 2021