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

1, 12, 18, 220, 396, 287532

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..6.

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

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

Sequence in context: A166627 A018957 A238922 * A110932 A112880 A211083

Adjacent sequences: A212125 A212126 A212127 * A212129 A212130 A212131

Keyword

nonn,more

Author

Omar E. Pol, Dec 19 2012

Status

approved