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using System.Collections.Generic;
using System.Numerics;
namespace Algorithms.Sequences;
/// <summary>
/// <para>
/// Sequence of the number of divisors of n, starting with 1.
/// </para>
/// <para>
/// OEIS: https://oeis.org/A000005.
/// </para>
/// </summary>
public class DivisorsCountSequence : ISequence
{
/// <summary>
/// Gets sequence of number of divisors for n, starting at 1.
/// </summary>
public IEnumerable<BigInteger> Sequence
{
get
{
yield return BigInteger.One;
for (var n = new BigInteger(2); ; n++)
{
var count = 2;
for (var k = 2; k < n; k++)
{
BigInteger.DivRem(n, k, out var remainder);
if (remainder == 0)
{
count++;
}
}
yield return count;
}
}
}
}
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