OFFSET
1,4
LINKS
Fintan Costello, Table of n, a(n) for n = 1..1000
FORMULA
a(n+1) = a(n)+b(n)+c(n), where b(n) is 1 if n is prime, 0 otherwise (sequence A010051) and c(n) is the number of primes less than the minimum prime factor of n. Since b(2n)=c(2n)=0 for all n>1 we see that a(2n+1)=a(2n) for all n>1. Taking d(n) to represent sequence A038802 we have a(2n)=a(2n-1)+c(2n-1)+d(n-1).
EXAMPLE
Example: For n=4 the only composite integers greater than or equal to 4 all of whose proper divisors are all less than 4 are 4,6, and 9. Since there are 3 such integers, a(4)=3.
MATHEMATICA
Join[{0}, Table[Length[Select[Range[n, n^2], ! PrimeQ[#] && Divisors[#][[-2]] < n &]], {n, 2, 100}]] (* T. D. Noe, Feb 28 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Fintan Costello, Feb 28 2011
STATUS
approved