A212658 Number of multisets {1^k1, 2^k2, ..., n^kn}, ki >= 0, with the sum of reciprocals <= 1.

1, 2, 4, 8, 17, 37, 86, 199, 475, 1138, 2769, 6748, 16613, 40904, 101317, 251401, 624958, 1555940, 3882708, 9701790, 24276866, 60817940, 152508653, 382828565, 961859364, 2418662434, 6086480305, 15327208770, 38622901484, 97384378728, 245686368946, 620158662562

Offset

0,2

Comments

The number of distinct sums of reciprocals is given by A212606.

Links

Dexter Senft, Table of n, a(n) for n = 0..36

Prog

(C#)
/* For n=43 or greater, the least common multiple of the numbers 1..n requires more than 64 bits to represent, and C# has no such native data type. */
using System;
using System.Collections.Generic;
namespace A212658 {
   class Program {
      static long Result;
      static long GCD(long n, long m) {
         long mod;
         long j = n<m ? m : n;
         long k = n<m ? n : m;
         while (true) if ((mod = k%j) == 0)
            return j; else { k=j; j=mod; }
      }
      static long LCM(int n) { // This produces A003418
         return n<=1 ? 1 : LCM(n-1) / GCD(LCM(n-1), n) * n;
      }
      static void Main(string[] args) {
         List<long> numbers = new List<long>();
         for (int n=1; n<=42; n++) {
            long lcm= LCM(n);
            numbers.Clear();
            Result = 0;
            for (int i=2; i<=n; i++) numbers.Add(lcm/i);
            Count(lcm, numbers, 0);
            Console.Write(n.ToString() + ": " + (Result+2).ToString() + "\n");
         }
      }
      static void Count(long Target, List<long> L, int At) {
         if (At >= L.Count) return;
         if (L[At] <= Target) {
            Result++;
            long AmtLeft = Target - L[At];
            if (AmtLeft >= L[L.Count-1]) Count(AmtLeft, L, At);
         }
         Count(Target, L, At+1);
         return;
      }
   }
}
/* Dexter Senft, Feb 07 2019 */

Crossrefs

Cf. A212657, A212606, A212607, A020473, A092669, A092671, A208480, A003418.

Sequence in context: A003426 A179476 A087803 * A036374 A214999 A348756

Adjacent sequences: A212655 A212656 A212657 * A212659 A212660 A212661

Keyword

nonn

Author

Max Alekseyev, May 23 2012

Extensions

a(24)-a(25) from Alois P. Heinz, Nov 20 2017

a(26)-a(31) from Dexter Senft, Feb 07 2019

Status

approved