OFFSET
2,2
COMMENTS
As p(k)/P(k)<=1, every positive integer is in this sequence. - Jon Perry, Jan 03 2013
LINKS
P. Erdős and J. H. van Lint, On the average ratio of the smallest and largest prime divisor of n, Nederl. Akad. Wetensch. Indag. Math. 44:2 (1982), pp. 127-132.
J. H. van Lint, Some sums involving the largest and smallest prime divisor of a natural number, CWI report ZW 25/74 (1974), 16 pp.
FORMULA
Erdős & Lint show that a(n) = n/log n + 3n/log^2 n + o(n/log^2 n). Lint had earlier shown that a(n) = o(n).
EXAMPLE
a(6) = floor(2/2 + 3/3 + 2/2 + 5/5 + 2/3) = floor(4 + 2/3) = 4.
PROG
(PARI) s=0.; for(n=2, 99, f=factor(n)[, 1]; print1(floor(s+=f[1]/f[#f])", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Charles R Greathouse IV, Jan 02 2013
STATUS
approved