|
%I #13 Mar 28 2015 22:36:31
%S 2,4,8,15,16,32,39,42,45,55,64,75,84,87,114,117,126,128,135,168,170,
%T 183,225,228,247,252,256,258,261,275,294,295,336,340,342,351,375,378,
%U 405,410,456,504,507,512,516,549,583,588,605,672,675,680,684,756,774
%N Arithmetic mean of distinct primes dividing n is a power of 2 (powers of 2 are not left out).
%H Michael De Vlieger, <a href="/A070008/b070008.txt">Table of n, a(n) for n = 1..3000</a>
%e n=9189=3*1021, mean=(3+1021)/2=512.
%t ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] Do[s=Apply[Plus, ba[n]]/lf[n]; If[IntegerQ[Log[2, s]], Print[{n, s}]], {n, 2, 10000}]
%t fQ[n_] := Block[{pf = FactorInteger@ n}, Length@ pf == 1 && pf[[1, 1]] == 2]; Select[Range[2, 780], fQ[Total[First /@ FactorInteger@#]/PrimeNu@#] &] (* _Michael De Vlieger_, Mar 28 2015 *)
%Y Cf. A070005, A070006, A070007, A008472, A001414.
%K nonn
%O 1,1
%A _Labos Elemer_, Apr 11 2002
|
