A038034 Number of compositions (ordered partitions) of 1 into {1/1, 1/2, 1/3, ..., 1/n}.

1, 2, 3, 7, 8, 52, 53, 288, 1209, 5247, 5248, 71395, 71396, 375779, 6957533, 52310862, 52310863, 1152622553, 1152622554, 45575902465, 1296407854551, 1580527987951, 1580527987952, 73245316681199, 584407520822198, 639887219617512, 11355804443049274, 516959218512416104, 516959218512416105, 29213061562205847736, 29213061562205847737, 886912328033731357358, 31286298736622399674197, 31349361777225437765677

Offset

1,2

Comments

a(n) = number of Egyptian fractions 1 = 1/x_1 + ... + 1/x_k (for any k), with max{x_i}<=n.

Links

Table of n, a(n) for n=1..34.

Index entries for sequences related to Egyptian fractions

Formula

a(n) = Sum_{i=1..n} A092667(i).

a(p) = a(p-1) + 1 for p prime. - Chai Wah Wu, Dec 27 2024

Example

a(4) = 7 since there are seven compositions into parts {1/1, 1/2, 1/3, 1/4}:
1 = 1/1, 1 = 1/2 + 1/2, 1 = 1/3 + 1/3 + 1/3, 1 = 1/2 + 1/4 + 1/4, 1 = 1/4 + 1/2 + 1/4, 1 = 1/4 + 1/4 + 1/2, and 1 = 1/4 + 1/4 + 1/4 + 1/4.

Crossrefs

Cf. A002967, A020473, A092667, A092670.

Sequence in context: A288628 A064669 A068342 * A103173 A378270 A098863

Adjacent sequences: A038031 A038032 A038033 * A038035 A038036 A038037

Keyword

nonn,nice

Author

Christian G. Bower, Jun 15 1998

Extensions

More terms from Max Alekseyev, Mar 02 2004

Status

approved