%I
%S 6,8,10,14,15,21,22,26,33,34,35,38,39,46,51,55,57,58,62,65,69,74,77,
%T 82,85,86,87,91,93,94,95,106,111,115,118,119,122,123,129,133,134,141,
%U 142,143,145,146,155,158,159,161,166,177,178,183,185,187,194,201,202,203
%N Numbers n such that the sum of the divisors minus the sum of the prime factors (counted with multiplicity) is equal to n+1.
%C Equals A006881 union {8}.  _Franklin T. AdamsWatters_, Jun 26 2009
%H Jayanta Basu, <a href="/A161918/b161918.txt">Table of n, a(n) for n = 1..10000</a>
%e n=21: Sum_divisors (1,3,7,21) = 32; Sum_prime_factors (3,7) = 10 > 3210 = 22. n=55: Sum_divisors (1,5,11,55) = 72; Sum_prime_factors (5,11) = 16 > 7216 = 56.
%p with(numtheory); P:=proc(i) local b,c,j,s,n; for n from 2 by 1 to i do b:=(convert(ifactors(n),`+`)1); c:=nops(b); j:=0; s:=0; for j from c by 1 to 1 do s:=s+convert(b[j],`*`); od; if n=sigma(n)s1 then print(n); fi; od; end: P(500);
%t Select[Range[203], DivisorSigma[1, #]  Total[Times @@@ FactorInteger[#]] == # + 1 &] (* _Jayanta Basu_, Aug 11 2013 *)
%o (PARI from _M. F. Hasler_):
%o isA161918(n)={ n+1 == sigma(n)(n=factor(n))[,1]~*n[,2] }
%o for(n=1,500, isA161918(n)&print1(n","))
%Y Cf. A161917, A006881, A151797, A030229.
%K easy,nonn
%O 1,1
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 23 2009
%E Edited by _N. J. A. Sloane_, Jun 27 2009 incorporating suggestions from _R. J. Mathar_, _M. F. Hasler_, _Benoit Jubin_ and others.
