A185222 Composite numbers m such that (m'+1)' = m', where m' = A003415(m) is the arithmetic derivative of m.

6, 42, 1806, 2786, 47058, 73178, 85082, 2143066830, 2214502422, 3138798830, 4404051298, 4428107218, 4428595298, 52495396602, 62994475914, 76852598955, 104971651322

Offset

1,1

Comments

All primes are a solution to this equation.

Number m is a term iff m' + 1 is a primary pseudoperfect number (A054377). - Max Alekseyev, Sep 09 2025

Links

Table of n, a(n) for n=1..17.

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, A054377, A203618.

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

a(14)-a(17) from Max Alekseyev, Sep 09 2025

Status

approved