A164829 a(1) = 2; a(n) for n > 1 is the smallest k > a(n-1) such that the harmonic mean of the divisors of k is one of the previous terms a(1), ..., a(n-1).

2, 6, 270, 2701389600, 71271827200

Offset

1,1

Comments

The harmonic mean of the divisors of k is k*A000005(k)/A000203(k). a(n) for n > 1 is a harmonic number, a term of A001599. Is the sequence finite ?

Similar sequences are obtained for other values of a(1). E.g. a(1) = 5 gives 5, 140, 496, 164989440, 28103080287744; a(1) = 8 gives 8, 672, 183694492800, 7322605472000.

Links

Table of n, a(n) for n=1..5.

Takeshi Goto, Table of A001599(n) for n=1..937

Example

The smallest number with harmonic mean of divisors = 2 is 6, hence a(2) = 6.
The next number with harmonic mean of divisors in {2, 6} is 270, hence a(3) = 270.

Crossrefs

Cf. A000005 (sigma_0, number of divisors), A000203 (sigma, sum of divisors), A001599 (harmonic or Ore numbers).

Sequence in context: A199125 A232696 A007190 * A028337 A215293 A264410

Adjacent sequences: A164826 A164827 A164828 * A164830 A164831 A164832

Keyword

nonn,hard,more

Author

Jaroslav Krizek, Aug 27 2009

Extensions

Edited and listed terms verified (using Takeshi Goto's list) by Klaus Brockhaus, Sep 04 2009

Status

approved