A230544 - OEIS

%I #4 Oct 27 2013 02:34:33

%S 1,1255,4063,5359,6583,8615,11623,12047,14359,14863,15943,27644,32471,

%T 49271,52607,81599,98471,101687,117647,164327,173447,176471,203327,

%U 209207,235271,246647,277271,301607,343271,355871,358367,360623,378047,392471,401927,406607

%N Solutions of the equation n'' = tau(n) * n', where n' and n'' are the first and the second arithmetic derivative of n.

%e For n = 6583 we have tau(n) = 4, n’ =  256, n’’= 1024 and 1024 = 4 * 256.

%p with(numtheory); P:= proc(q) local a1, a2, n, p;

%p for n from 1 to q do a1:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]); ;

%p a2:=a1*add(op(2,p)/op(1,p),p=ifactors(a1)[2]);

%p if a2=tau(n)*a1 then print(n); fi; od; end: P(10^6);

%Y Cf. A000005, A003415, A068346.

%K nonn

%O 1,2

%A _Paolo P. Lava_, Oct 25 2013