

A020473


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


12



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
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OFFSET

1,2


COMMENTS

Number of ways to represent 1 = sum_{k=1}^n b(k)/k, where the b(k) >= 0.  Franklin T. AdamsWatters, Aug 01 2006


LINKS

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


FORMULA

a(n) = Sum(A092666(i), i=1..n).
For prime p, a(p) = a(p1) + 1. [From Max Alekseyev, May 07 2012]


MATHEMATICA

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


CROSSREFS

Cf. A038034, A092670, A208480.
Sequence in context: A075372 A064725 A100330 * A098833 A075371 A218948
Adjacent sequences: A020470 A020471 A020472 * A020474 A020475 A020476


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



