

A182843


Number of composite integers greater than or equal to n whose proper divisors are all less than n.


2



0, 0, 1, 3, 3, 6, 6, 10, 10, 11, 11, 16, 16, 22, 22, 23, 23, 30, 30, 38, 38, 39, 39, 48, 48, 50, 50, 51, 51, 61, 61, 72, 72, 73, 73, 75, 75, 87, 87, 88, 88, 101, 101, 115, 115, 116, 116, 131, 131, 134, 134, 135, 135, 151, 151, 153, 153, 154, 154, 171, 171, 189, 189, 190, 190, 192, 192, 211, 211
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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(2n1)+c(2n1)+d(n1).


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

Cf. A010051, A038802.
Sequence in context: A290966 A049318 A079551 * A008805 A188270 A026925
Adjacent sequences: A182840 A182841 A182842 * A182844 A182845 A182846


KEYWORD

nonn


AUTHOR

Fintan Costello, Feb 28 2011


STATUS

approved



