OFFSET
1,2
COMMENTS
A positive integer n belongs to the sequence if and only the number of its divisors (d(n)) is >= the average number of divisors, in the range from 1 through n, for all positive integers (H(n)).
Visible sharp bend on the graph around the 800th term occur where the n-th harmonic number exceeds 8. - Ivan Neretin, Oct 16 2016
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..5000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 840. (d(n) is given as sigma_0(n).)
EXAMPLE
6 is in the sequence because the number of its divisors, 4, is greater than the 6th harmonic number, 1/1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 = 2.45.
MATHEMATICA
ok[n_] := DivisorSigma[0, n] >= HarmonicNumber[n]; Select[ Range[132], ok] (* Jean-François Alcover, Sep 19 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Matthew Vandermast, May 29 2004
STATUS
approved