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A187737
a(n) = floor(sum_{1 < k <= n} p(k)/P(k)), where p(k) is the smallest prime factor of k and P(k) is the largest prime factor of k.
0
1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 9, 10, 11, 11, 12, 13, 14, 15, 15, 16, 16, 17, 17, 18, 19, 20, 20, 21, 21, 22, 23, 24, 24, 24, 25, 26, 26, 26, 27, 28, 28, 29, 29, 30, 30, 31, 32, 33, 33, 33, 33, 34, 35, 35, 36, 36, 36, 37, 37, 38
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OFFSET
2,2
COMMENTS
As p(k)/P(k)<=1, every positive integer is in this sequence. -
Jon Perry
, Jan 03 2013
LINKS
Table of n, a(n) for n=2..61.
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
Sequence in context:
A171974
A232748
A308936
*
A109401
A307294
A280471
Adjacent sequences:
A187734
A187735
A187736
*
A187738
A187739
A187740
KEYWORD
nonn
AUTHOR
Charles R Greathouse IV
, Jan 02 2013
STATUS
approved