OFFSET
1,1
COMMENTS
In 1919, George Polya conjectured that O(n) >= E(n) for n >= 2. However, in 1958, C. B. Haselgrove showed that there are infinitely many positive integers n for which O(n) < E(n). In 1966, R.S. Lehman showed that 906180359 is the smallest positive integer for which O(n) = E(n) - 1. (Tattersall, p. 92)
REFERENCES
J. Tattersall, "Elementary Number Theory in Nine Chapters". Cambridge University Press, 2001.
MATHEMATICA
(*This program relies on Lehman's result that 906180359 is the least term of the sequence.*) Omega[n_] := Apply[Plus, Transpose[FactorInteger[n]][[2]]]; start = 906180360; l = {906180359}; o = 0; e = 1; i = start; While[i < 906193475, If[Mod[Omega[i], 2] == 0, e = e + 1, o = o + 1]; If[o == e - 1, l = Append[l, i]]; i = i + 1]; l
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Oct 30 2002
STATUS
approved