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;
                }
            }
        }
    }
}