A276701 - OEIS

%I #7 Sep 20 2016 13:18:40

%S 1,3,6,20259,43912,563103,18895035,119847148,305478634710

%N Numbers n>0 such that n’ = (n-1)’ + (n-2)’, where n’ is the arithmetic derivative of n.

%C a(10) > 5*10^12. - _Giovanni Resta_, Sep 16 2016

%e 6’ = 5, 5’ = 1, 4’ = 4 and 5 = 1 + 4.

%p with(numtheory): P:= proc(q) local a,b,c,n,p;

%p a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);

%p b:=(n-1)*add(op(2,p)/op(1,p),p=ifactors(n-1)[2]);

%p c:=(n-2)*add(op(2,p)/op(1,p),p=ifactors(n-2)[2]);

%p if a=b+c then print(n); fi; od; end: P(10^9);

%Y Cf. A003415.

%K nonn,more

%O 1,2

%A _Paolo P. Lava_, Sep 15 2016

%E a(9) from _Giovanni Resta_, Sep 16 2016