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 A079125 #12 Apr 16 2025 05:29:26
%S A079125 1,1,1,2,3,5,5,13,13,27,14,89,21,89,97,230,45,613,63,980,347,580,121,
%T A079125 6663,330,1289,1043,5847,295,26488,389,12813,2800,5411,2840,156304,
%U A079125 863,10433,6939,161711,1425,272499,1815,103738,61469,35448,2909,2475011
%N A079125 Number of ways to partition the sum of all divisors of n (sigma(n), A000203) into distinct positive integers not greater than n.
%H A079125 Amiram Eldar, <a href="/A079125/b079125.txt">Table of n, a(n) for n = 1..1000</a>
%F A079125 a(n) = b(0, n), b(m, n) = 1 + Sum_{m < i < j < n & i+j = sigma(n)} b(i, j).
%t A079125 a[n_] := Module[{sum = DivisorSigma[1, n], x}, CoefficientList[Product[1 + x^i, {i, 1, n}], x][[1 + sum]]]; Array[a, 50] (* _Amiram Eldar_, Apr 15 2025 *)
%o A079125 (PARI) a(n)=my(v=partitions(sigma(n),n));sum(i=1,#v,#vecsort(v[i],,8)==#v[i]) \\ _Charles R Greathouse IV_, Feb 14 2013
%Y A079125 Cf. A079126, A000009, A079122, A079124, A067953.
%K A079125 nonn
%O A079125 1,4
%A A079125 _Reinhard Zumkeller_, Dec 27 2002