A185222 Composite numbers n such that (n'+1)' = n', where n' is the arithmetic derivative of n.

6, 42, 1806, 2786, 47058, 73178, 85082, 2143066830, 2214502422, 3138798830, 4404051298, 4428107218, 4428595298

Offset: 1

Author

José María Grau Ribas, Jan 24 2012

Keywords

• nonn
• more

Comments

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

No more terms below 4.8*10^10. - Amiram Eldar, Oct 18 2019

Crossrefs

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

Programs

Mathematica

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]&]

Extensions

a(8)-a(13) from Amiram Eldar, Oct 18 2019