A050781 Numbers k such that sopfr(k) = sopfr(k - sopfr(k)).

55, 72, 84, 119, 143, 256, 2106, 2211, 2279, 3024, 3150, 3551, 4284, 6360, 6500, 9350, 10200, 10285, 10919, 13560, 14279, 14351, 15606, 16463, 17063, 23595, 25011, 27208, 28208, 28600, 31460, 33096, 42180, 44330, 52320, 53053, 53824

Offset: 0

Author

Patrick De Geest, Sep 15 1999

Keywords

• nonn
• nice

Comments

sopfr(k) = sum of the prime factors of k (with multiplicity).

Examples

			sopfr(72) = 2+2+2+3+3 = 12 = 2+2+3+5 = sopfr(72 - sopfr(72)), so 72 is in the sequence.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A001414, A050703-A050710, A050780.

Programs

Mathematica

sopf[n_]:=Module[{sopfn=Total[Times@@@FactorInteger[n]],m},m=n+sopfn;If[n==m-Total[Times@@@FactorInteger[m]],m,0]]; DeleteCases[Table[ sopf[n],{n,55000}],?(#==0&)] (* _Harvey P. Dale, Jun 15 2011 *)

Extensions

Edited by Jon E. Schoenfield, Dec 25 2016