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 A073185 #46 Sep 14 2020 02:58:31
%S A073185 1,3,4,7,6,12,8,7,13,18,12,28,14,24,24,7,18,39,20,42,32,36,24,28,31,
%T A073185 42,13,56,30,72,32,7,48,54,48,91,38,60,56,42,42,96,44,84,78,72,48,28,
%U A073185 57,93,72,98,54,39,72,56,80,90,60,168,62,96,104,7,84,144,68,126,96,144,72
%N A073185 Sum of cubefree divisors of n.
%C A073185 Sum of divisors of the cubefree kernel of n (see first formula).
%H A073185 Reinhard Zumkeller, <a href="/A073185/b073185.txt">Table of n, a(n) for n = 1..10000</a>
%F A073185 a(n) = A000203(A007948(n)).
%F A073185 a(n) <= A073183(n).
%F A073185 Multiplicative with a(p) = 1+p, a(p^e) = 1 + p + p^2, e>1. - _Christian G. Bower_, May 18 2005
%F A073185 a(n) = sum(A212793(A027750(n,k)) * A027750(n,k): k=1..A000005(n)). - _Reinhard Zumkeller_, May 27 2012
%F A073185 Dirichlet g.f.: zeta(s)*zeta(s-1)/zeta(3s-3). - _R. J. Mathar_, Apr 12 2011
%F A073185 Sum_{k=1..n} a(k) ~ Pi^2 * n^2 / (12*Zeta(3)). - _Vaclav Kotesovec_, Feb 01 2019
%e A073185 The divisors of 56 are {1, 2, 4, 7, 8, 14, 28, 56}, 8=2^3 and 56=7*2^3 are not cubefree, therefore a(56) = 1 + 2 + 4 + 7 + 14 + 28 = 56.
%p A073185 charFfree := proc(n,t) local f; for f in ifactors(n)[2] do if op(2,f) >= t then return 0 ; end if; end do: return 1 ; end proc:
%p A073185 A073185 := proc(n) add( d*charFfree(d,3),d =numtheory[divisors](n) ); end proc: # _R. J. Mathar_, Apr 12 2011
%t A073185 nn = 71;f[list_, i_] := list[[i]]; a =Table[If[Max[FactorInteger[n][[All, 2]]] <= 2, n, 0], {n, 1, nn}]; b = Table[1, {nn}]; Select[Table[DirichletConvolve[f[a, n], f[b, n], n, m], {m, 1, nn}], # > 0 &] (* _Geoffrey Critzer_, Mar 22 2015 *)
%t A073185 f[p_, e_] := 1 + p + If[e > 1, p^2, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Sep 14 2020 *)
%o A073185 (Haskell)
%o A073185 a073185 = sum . filter ((== 1) . a212793) . a027750_row
%o A073185 -- _Reinhard Zumkeller_, May 27 2012
%o A073185 (PARI) a(n) = {my(f=factor(n)); for (i=1, #f~, p = f[i,1]; if ((e=f[i,2]) == 1, f[i,1] = 1+p, f[i,1] = 1+p+p^2); f[i,2] = 1;); factorback(f);} \\ _Michel Marcus_, Feb 06 2015
%Y A073185 Cf. A000203, A073184, A004709, A073182, A073181, A048250.
%K A073185 nonn,mult
%O A073185 1,2
%A A073185 _Reinhard Zumkeller_, Jul 19 2002
%E A073185 Incorrect comment removed by _Álvar Ibeas_, Feb 06 2015