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A070008
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Arithmetic mean of distinct primes dividing n is a power of 2 (powers of 2 are not left out).
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2
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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n=9189=3*1021, mean=(3+1021)/2=512.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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