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

1,1

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

Links

Table of n, a(n) for n=1..13.

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]&]

Crossrefs

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

Sequence in context: A273922 A139223 A291192 * A179861 A083940 A101071

Adjacent sequences: A185219 A185220 A185221 * A185223 A185224 A185225

Keyword

nonn,more

Author

José María Grau Ribas, Jan 24 2012

Extensions

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

Status

approved