A185222 - OEIS

A185222

Composite numbers n such that (n'+1)' = n', where n' is the arithmetic derivative of n.

%I #19 Oct 18 2019 11:25:47

%S 6,42,1806,2786,47058,73178,85082,2143066830,2214502422,3138798830,

%T 4404051298,4428107218,4428595298

%N Composite numbers n such that (n'+1)' = n', where n' is the arithmetic derivative of n.

%C All primes are a solution to this equation. For composite numbers, a(8) > 10^7.

%C No more terms below 4.8*10^10. - _Amiram Eldar_, Oct 18 2019

%t dn[0]=0; dn[1]=0; dn[n_] := Module[{f=Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus@@(n*f[[2]]/f[[1]])]]; Select[Range[2,100000], !PrimeQ[#] && dn[#] == dn[dn[#]+1]&]

%Y Cf. A003415, A203618 (solutions of the differential equation (n'-1)' = n-1).

%K nonn,more

%O 1,1

%A _José María Grau Ribas_, Jan 24 2012

%E a(8)-a(13) from _Amiram Eldar_, Oct 18 2019