A212128 Nonprimes whose arithmetic derivative equals the sum of its proper divisors.

1, 12, 18, 220, 396, 287532

Offset: 1

Author

Omar E. Pol, Dec 19 2012

Keywords

• nonn
• more

Comments

a(7) > 10^12. - Giovanni Resta, Mar 11 2014

Examples

			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.
		

Crossrefs

Cf. A018252, A000203, A001065, A003415, A211991, A212127.

Programs

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 *)