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 A111865 #38 Aug 05 2025 22:55:54
%S A111865 1,1,1,2,3,3,5,7,9,11,14,17,24,29,36,46,57,66,85,103,125,151,182,213,
%T A111865 264,310,368,440,524,604,724,849,998,1164,1363,1573,1854,2136,2481,
%U A111865 2879,3336,3807,4427,5079,5844,6698,7695,8754,10072,11451,13075,14898,16988
%N A111865 Expansion of g.f. Product_{k>=1} 1/(1-x^sigma(k)).
%C A111865 Number of partitions of n into parts of size p = sigma(k) for some k, when there are A054973(p) kinds of part p.
%H A111865 Alois P. Heinz, <a href="/A111865/b111865.txt">Table of n, a(n) for n = 0..10000</a> (first 1001 terms from Seiichi Manyama)
%F A111865 G.f.: Product_{k>=1} 1/(1-x^sigma(k)).
%e A111865 a(6) = 5 : We have sigma(1)=1, sigma(2)=3, sigma(3)=4, sigma(5)=6 so 111111, 1113, 114, 6 and 33.
%p A111865 with(numtheory):
%p A111865 seq(coeff(series(mul(1/(1-x^sigma(k)),k=1..n), x,n+1),x,n),n=0..60); # _Muniru A Asiru_, May 31 2018
%t A111865 CoefficientList[ Series[Product[1/(1 - x^DivisorSigma[1, k]), {k, 47}], {x, 0, 52}], x] (* _Robert G. Wilson v_, Nov 25 2005 *)
%o A111865 (PARI) lista(nn) = Vec(prod(k=1, nn, 1/(1-x^sigma(k))+ O(x^nn))) \\ _Michel Marcus_, May 30 2018
%Y A111865 Cf. A000203, A002191, A007609, A054973, A305320.
%K A111865 nonn
%O A111865 0,4
%A A111865 _Jon Perry_, Nov 23 2005
%E A111865 More terms from _Robert G. Wilson v_, Nov 25 2005
%E A111865 a(0)=1 prepended by _Seiichi Manyama_, May 30 2018