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A212128
Nonprimes whose arithmetic derivative equals the sum of its proper divisors.
2
1, 12, 18, 220, 396, 287532
OFFSET
1,2
COMMENTS
a(7) > 10^12. - Giovanni Resta, Mar 11 2014
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Omar E. Pol, Dec 19 2012
STATUS
approved