%I
%S 84,132,168,228,234,252,260,264,276,308,336,340,372,396,456,468,504,
%T 516,520,528,532,552,558,564,580,588,616,644,672,680,684,702,708,740,
%U 744,756,792,804,820,828,836,852,855,868,884,912,936,948,996,1008,1012,1032
%N Numbers such that gcd(Sum,n) = A099635 and gcd(Sum,Product) = A099636 are not identical. Sum and Product here are the sum and product of all distinct prime factors of n.
%C Of the first million integers, 75811 (of which 6300 are odd) belong to this sequence.  _Robert G. Wilson v_, Nov 04 2004
%e 84 is here because its factor list = {2,3,7} and sum = 2 + 3 + 7 = 12, product = 2*3*7 = 42, gcd(12,84) = 12, gcd(12,42) = 6 != 12.
%t <<NumberTheory`NumberTheoryFunctions` pf[x_] :=PrimeFactorList[x];a=Table[Max[pf[w]], {w, 2, m}]; Table[GCD[Apply[Plus, pf[w]], Apply[Plus, pf[w]]], {w, 1, 100}]
%t PrimeFactors[n_Integer] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; fQ[n_] := Block[{pf = PrimeFactors[n]}, GCD[Plus @@ pf, n] == GCD[Plus @@ pf, Times @@ pf]]; Select[ Range[1039], ! fQ[ # ] &] (* _Robert G. Wilson v_, Nov 04 2004 *)
%Y Cf. A099634, A099635, A099636.
%K nonn
%O 1,1
%A _Labos Elemer_, Oct 28 2004
%E More terms from _Robert G. Wilson v_, Nov 04 2004
