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A152188
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a(0) = 0, a(n) is the number of divisors of n that are greater than a(n-1).
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1
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0, 1, 1, 1, 2, 1, 3, 1, 3, 1, 3, 1, 5, 1, 3, 2, 3, 1, 5, 1, 5, 2, 2, 1, 7, 1, 3, 2, 4, 1, 7, 1, 5, 2, 2, 3, 6, 1, 3, 2, 6, 1, 7, 1, 5, 3, 2, 1, 9, 1, 5, 2, 4, 1, 7, 2, 6, 2, 2, 1, 11, 1, 3, 4, 4, 3, 5, 1, 5, 2, 6, 1, 11, 1, 3, 4, 3, 3, 5, 1, 9, 2, 2, 1, 11, 2, 2, 3, 6, 1, 11, 2, 4, 2, 2, 3, 9, 1, 5, 4, 6, 1, 7, 1, 7, 4
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OFFSET
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0,5
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COMMENTS
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a(n) for prime n equals 1, but a value of 1 does not imply primality (e.g., a(9) = 1 but 9 is the square of a prime).
a(n) = 1 does imply the primality of n if n > 1260. (see Math StackExchange link)
a(n) can never exceed floor(n/2) for n > 1.
a(n) for even n greater than 2 can never equal 1.
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LINKS
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EXAMPLE
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For n = 6, we have a(n) = 3 as 2, 3, and 6 are greater than 1 and 1 = a(5).
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MATHEMATICA
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a[0] := 0; a[n_] := a[n] = Length[Select[Divisors[n], # > a[n - 1] &]]; Table[a[n], {n, 0, 99}] (* Alonso del Arte, Sep 24 2011 *)
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PROG
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(Java)
import java.util.Set; import java.util.TreeSet;
public class Seq1 { public static final int TOCALC = 50; public static void main(String[] args) { int[] terms = new int[TOCALC]; terms[0] = 0; terms[1] = 1; Set<Integer> uniqueFactors = new TreeSet<Integer>(); for(int n = 2; n <= TOCALC - 1; n++){ for(int i = 1; i <= n; i++){ if(n % i == 0){ uniqueFactors.add(i); } } int counter = 0; for(int test : uniqueFactors){ if(test > terms[n - 1]){ counter++; } } terms[n] = counter; uniqueFactors.clear(); } int newLine = 0; for(int d = 0; d <= TOCALC - 1; d++){ System.out.print(terms[d] + ", "); newLine++; if(newLine == 10){ System.out.println(); newLine = 0; } } int max = 0; for(int f = 0; f <= TOCALC - 1; f++){ max = Math.max(max, terms[f]); } System.out.println(); System.out.print("Max: " + max); }}
(PARI)
up_to = 105;
v152188 = vector(up_to);
v152188[1] = 1;
A152188(n) = if(n<=1, n, my(prev = v152188[n-1], res = sumdiv(n, d, (d>prev))); v152188[n] = res; (res)); \\ Must be called in order of increasing n.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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