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A185222 Composite numbers n such that (n'+1)' = n', where n' is the arithmetic derivative of n. 1
6, 42, 1806, 2786, 47058, 73178, 85082, 2143066830, 2214502422, 3138798830, 4404051298, 4428107218, 4428595298 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 13 16:17 EDT 2021. Contains 345008 sequences. (Running on oeis4.)