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 A007430 M3750 #57 Feb 19 2024 01:50:39
%S A007430 1,5,6,16,8,30,10,42,24,40,14,96,16,50,48,99,20,120,22,128,60,70,26,
%T A007430 252,46,80,82,160,32,240,34,219,84,100,80,384,40,110,96,336,44,300,46,
%U A007430 224,192,130,50,594,76,230,120,256,56,410,112,420,132,160,62,768,64,170,240,466,128,420
%N A007430 Inverse Moebius transform applied thrice to natural numbers.
%C A007430 a(n) = A000027(n) * A000012(n) * A000012(n) * A000012(n) = A000027(n) * A000012(n) * A000005(n) = A000203(n) * A000005(n) = A000203(n) * A000012(n) * A000012(n) = A007429(n) * A000012(n), where operation * denotes Dirichlet convolution for n >= 1. Dirichlet convolution of functions b(n), c(n) is function a(n) = b(n) * c(n) = Sum_{d|n} b(d)*c(n/d). - _Jaroslav Krizek_, Mar 20 2009
%D A007430 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007430 T. D. Noe, <a href="/A007430/b007430.txt">Table of n, a(n) for n = 1..10000</a>
%H A007430 O. Bordelles, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Bordelles2/bordelles61.html">Mean values of generalized gcd-sum and lcm-sum functions</a>, JIS 10 (2007) 07.9.2, sequence g_5.
%H A007430 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A007430 a(n) = Sum_{d|n} sigma(d)*tau(n/d). - _Benoit Cloitre_, Mar 03 2004
%F A007430 Multiplicative with a(p^e) = Sum_{k=0..e} binomial(e-k+2, e-k)*p^k.
%F A007430 Dirichlet g.f.: zeta(s-1)*zeta^3(s).
%F A007430 Sum_{k=1..n} a(k) ~ Pi^6 * n^2 / 432. - _Vaclav Kotesovec_, Nov 06 2018
%t A007430 a[n_] := Total[ DivisorSigma[1, #]*DivisorSigma[0, n/#]& /@ Divisors[n]]; Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Nov 15 2011 *)
%o A007430 (PARI) a(n)=sumdiv(n,d,sigma(d)*numdiv(n/d))
%o A007430 (PARI) a(n)=if(n<1,0,direuler(p=2,n,1/(1-X)^3/(1-p*X))[n]) /* _Ralf Stephan_ */
%o A007430 (PARI) a(n)=sumdiv(n, x, sumdiv(x, y, sumdiv(y, z, z ) ) ); /* _Joerg Arndt_, Oct 07 2012 */
%o A007430 (Haskell)
%o A007430 a007430 n = sum $ zipWith (*) (map a000005 ds) (map a000203 $ reverse ds)
%o A007430 where ds = a027750_row n
%o A007430 -- _Reinhard Zumkeller_, Aug 02 2014
%Y A007430 Cf. A000005, A000203, A027750.
%K A007430 nonn,easy,nice,mult
%O A007430 1,2
%A A007430 _N. J. A. Sloane_