A070008 Arithmetic mean of distinct primes dividing n is a power of 2 (powers of 2 are not left out).

2, 4, 8, 15, 16, 32, 39, 42, 45, 55, 64, 75, 84, 87, 114, 117, 126, 128, 135, 168, 170, 183, 225, 228, 247, 252, 256, 258, 261, 275, 294, 295, 336, 340, 342, 351, 375, 378, 405, 410, 456, 504, 507, 512, 516, 549, 583, 588, 605, 672, 675, 680, 684, 756, 774

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..3000

Example

n=9189=3*1021, mean=(3+1021)/2=512.

Mathematica

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}]
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 *)

Crossrefs

Cf. A070005, A070006, A070007, A008472, A001414.

Sequence in context: A140117 A328677 A039743 * A033623 A094398 A277728

Adjacent sequences: A070005 A070006 A070007 * A070009 A070010 A070011

Keyword

nonn

Author

Labos Elemer, Apr 11 2002

Status

approved