A020473 Egyptian fractions: number of partitions of 1 into reciprocals of positive integers <= n.

1, 2, 3, 5, 6, 13, 14, 24, 34, 60, 61, 168, 169, 252, 627, 1011, 1012, 2430, 2431, 7212, 15024, 16553, 16554, 50219, 60008, 64284, 92071, 260178, 260179, 844846, 844847, 1431187, 2608883, 2661217, 7946814, 22692855, 22692856, 22911815, 36004488, 120859171

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Number of ways to represent 1 = Sum_{k=1..n} b(k)/k, where the b(k) >= 0. - Franklin T. Adams-Watters, Aug 01 2006

Links

• Toshitaka Suzuki, Table of n, a(n) for n = 1..390
• Index entries for sequences related to Egyptian fractions

Crossrefs

Cf. A038034, A092666, A092670, A208480.

Programs

Mathematica

Table[Length[IntegerPartitions[1, All, 1/Range[n]]], {n, 1, 20}] (* Ben Branman, Apr 21 2012 *)

Formula

a(n) = Sum(A092666(i), i=1..n).

For prime p, a(p) = a(p-1) + 1. - Max Alekseyev, May 07 2012