A070007 -id:A070007 - cp's OEIS frontend

A144710 Erroneous version of A070007.

15, 65, 77, 87, 247, 285, 301, 357, 481

Offset: 1

dead

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

Labos Elemer, Apr 11 2002

nonn

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

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

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

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 *)

A070009 Least number m such that the arithmetic mean of the distinct prime divisors of m is equal to 2^n.

Original entry on oeis.org

2, 15, 39, 87, 183, 2071, 1255, 1527, 3063, 18402, 12279, 106327, 49143, 622231, 589794, 1703767, 1310695, 9961111, 3145719, 31457210, 12582903, 310377127, 50331639, 2046816631, 335544295, 10603194271, 8858369762, 1610612727, 44023413103, 40802188951

Offset: 1

Labos Elemer, Apr 11 2002

nonn

Are there any terms with more than 3 prime factors? - David Wasserman, May 05 2003

			a(15) = 589794 because m = 2*3*98299; mean = (2+3+98299)/3 = 32768 = 2^15.

Cf. A070005, A070006, A070007, A070008, A070009, A008472, A001414, A001221.

a = Table[0, {21}]; Do[b = Transpose[ FactorInteger[n]][[1]]; c = Log[2, Apply[ Plus, b] / Length[b]]; If[ IntegerQ[c] && a[[c]] == 0, a[[c]] = n], {n, 2, 10^8/3}]; a

a(n) = Min{x; A008472(x)/A001221(x)=2^n}.

Edited and extended by Robert G. Wilson v, Apr 30 2002
More terms from David Wasserman, May 05 2003
a(29)-a(30) from Donovan Johnson, Aug 06 2012

cp's OEIS Frontend

A144710 Erroneous version of A070007.

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

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A070009 Least number m such that the arithmetic mean of the distinct prime divisors of m is equal to 2^n.

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