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%I #20 Mar 16 2024 11:19:44
%S 1,12,18,220,396,287532
%N Nonprimes whose arithmetic derivative equals the sum of its proper divisors.
%C a(7) > 10^12. - _Giovanni Resta_, Mar 11 2014
%e The arithmetic derivative of 12 is equal to 16 (see A003415). On the other hand the sum of proper divisors of 12 is equal to 16 since 1+2+3+4+6 = 16, so 12 is in the sequence.
%t dn[0] = 0; dn[1] = 0; dn[n_?Negative] := -dn[-n]; dn[n_] := Module[{f = Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus @@ (n*f[[2]]/f[[1]])]]; Select[Range[300000], ! PrimeQ[#] && dn[#] == DivisorSigma[1, #] - # &] (* _T. D. Noe_, Dec 27 2012 *)
%Y Cf. A018252, A000203, A001065, A003415, A211991, A212127.
%K nonn,more
%O 1,2
%A _Omar E. Pol_, Dec 19 2012