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.

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

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