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 A055225 #44 Jul 02 2025 16:01:59
%S A055225 1,3,4,9,6,24,8,41,37,68,12,258,14,192,384,593,18,1557,20,2794,2552,
%T A055225 2192,24,16730,3151,8388,20440,35394,30,116474,32,135457,178512,
%U A055225 131396,94968,1111035,38,524688,1596560,2530986,42,7280934,44,8403778
%N A055225 a(n) = Sum_{k divides n} (n/k)^k.
%C A055225 a(n) is the number of (nonempty) linear partitions of the linearly ordered set [n] = {1,2,...,n} with blocks of the same size, where each block has exactly one element marked. For instance, for n = 4, we have the following 9 linear partitions (where the marked elements are denoted by *):
%C A055225 . (*)(*)(*)(*), (*2)(*4), (*234),
%C A055225 . (*2)(3*), (1*34),
%C A055225 . (1*)(*4), (12*4),
%C A055225 . (1*)(3*), (123*).
%C A055225 - _Emanuele Munarini_, Feb 03 2014
%H A055225 Nick Hobson, <a href="/A055225/b055225.txt">Table of n, a(n) for n = 1..1000</a>
%F A055225 G.f.: Sum_{n>=1} -log(1 - n*x^n)/n = Sum_{n>=0} a(n) x^n/n. - _Paul D. Hanna_, Aug 04 2002
%F A055225 G.f.: Sum_{n>0} n*x^n/(1-n*x^n). - _Vladeta Jovovic_, Sep 02 2002
%F A055225 Sum_{k=1..n} a(k) ~ 3^((n + 3 - mod(n,3))/3)/2. - _Vaclav Kotesovec_, Aug 07 2022
%e A055225 a(10) = 10^1 + 5^2 + 2^5 + 1^10 = 68 because positive divisors of 10 are 1, 2, 5, 10.
%t A055225 Table[Total[Quotient[n, x = Divisors[n]]^x], {n, 44}] (* _Jayanta Basu_, Jul 08 2013 *)
%t A055225 Table[Sum[d^(n/d), {d, Divisors[n]}], {n, 1, 100}] (* _Emanuele Munarini_, Feb 03 2014 *)
%o A055225 (PARI) vector(44, n, sumdiv(n, d, (n/d)^d))
%o A055225 (PARI) a(n) = sumdiv(n,d, d^(n/d) ); \\ _Joerg Arndt_, Apr 14 2013
%o A055225 (Maxima) a(n) := lsum(d^(n/d), d, listify(divisors(n))); makelist(a(n), n, 1, 40); /* _Emanuele Munarini_, Feb 03 2014 */
%Y A055225 Cf. A005225, A038041, A236696.
%K A055225 nonn
%O A055225 1,2
%A A055225 _Leroy Quet_, Jun 20 2000
%E A055225 More terms from _James Sellers_, Jul 04 2000
%E A055225 Duplicate g.f. removed by _Franklin T. Adams-Watters_, Sep 01 2009