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

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

Author

Labos Elemer, Apr 11 2002

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

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

Programs

Mathematica

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

Formula

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

Extensions

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