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 A122697 #3 Mar 30 2012 17:35:16
%S A122697 0,2,3,2,7,5,15,14,24,28,56,52,101,105,155,189,297,310,490,536,747,
%T A122697 890,1255,1380,1930,2234,2928,3433,4565,5133,6842,7881,9975,11716,
%U A122697 14778,17006,21637,25035,30882,35972,44583,51200,63261,73115,88459,103048
%N A122697 Number of indecomposable partitions of n.
%C A122697 A partition is indecomposable if it is not [1] and cannot be represented as the product of two smaller partitions, where the product of two partitions is the multiset of all products of parts from the two multiplicands. Another way to define the product of partitions is to regard the partition as a finite sequence b(k) being the number of parts of size k; then the Dirichlet g.f. of b * c is the product of the Dirichlet g.f.s of b and c.
%F A122697 The (formal) Dirichlet generating function for A000041 is Product_{n>1} 1/(1-n^{-s})^a(n). (Formal because this g.f. does not converge for any value of s.)
%e A122697 The product of [2,2,1] * [2,1,1] is the partition with parts:
%e A122697 4 4 2
%e A122697 2 2 1
%e A122697 2 2 1
%e A122697 which is [4^2,2^5,1^2]. In terms of Dirichlet g.f.s, this is (2*2^s + 1^s) * (2^s + 2*1^s) = (2*4^s + 5*2^s + 2*1^s).
%e A122697 Of the partitions of 6, [6] = [3] * [2], [4,2] = [2] * [2,1], [3^2] = [3] * [1^2], [2^3] = [2] * [1^3], [2^2,1^2] = [2,1] * [1^2] and [1^6] = [1^3] * [1^2]. This leaves [5,1], [4,1^2], [3,2,1], [3,1^3] and [2,1^4] as the 5 indecomposable partitions of 6.
%Y A122697 Cf. A000041, A090751.
%K A122697 nonn
%O A122697 1,2
%A A122697 _Franklin T. Adams-Watters_, Sep 22 2006