This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A038034 #21 Dec 28 2024 03:06:02
%S A038034 1,2,3,7,8,52,53,288,1209,5247,5248,71395,71396,375779,6957533,
%T A038034 52310862,52310863,1152622553,1152622554,45575902465,1296407854551,
%U A038034 1580527987951,1580527987952,73245316681199,584407520822198,639887219617512,11355804443049274,516959218512416104,516959218512416105,29213061562205847736,29213061562205847737,886912328033731357358,31286298736622399674197,31349361777225437765677
%N A038034 Number of compositions (ordered partitions) of 1 into {1/1, 1/2, 1/3, ..., 1/n}.
%C A038034 a(n) = number of Egyptian fractions 1 = 1/x_1 + ... + 1/x_k (for any k), with max{x_i}<=n.
%H A038034 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%F A038034 a(n) = Sum_{i=1..n} A092667(i).
%F A038034 a(p) = a(p-1) + 1 for p prime. - _Chai Wah Wu_, Dec 27 2024
%e A038034 a(4) = 7 since there are seven compositions into parts {1/1, 1/2, 1/3, 1/4}:
%e A038034 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.
%Y A038034 Cf. A002967, A020473, A092667, A092670.
%K A038034 nonn,nice
%O A038034 1,2
%A A038034 _Christian G. Bower_, Jun 15 1998
%E A038034 More terms from _Max Alekseyev_, Mar 02 2004