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 A097378 #12 Feb 16 2025 08:32:54
%S A097378 2,5,10,9,26,37,50,9,28,101,122,73,170,197,226,9,290,109,362,201,442,
%T A097378 485,530,73,126,677,28,393,842,901,962,9,1090,1157,1226,217,1370,1445,
%U A097378 1522,201,1682,1765,1850,969,676,2117,2210,73,344,501,2602,1353,2810
%N A097378 a(n) = SquareFreeKernel(n)*CubeFreeKernel(n) + 1.
%H A097378 Amiram Eldar, <a href="/A097378/b097378.txt">Table of n, a(n) for n = 1..10000</a>
%H A097378 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Cubefree.html">Cubefree</a>.
%H A097378 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squarefree.html">Squarefree</a>.
%F A097378 a(n) = A007947(n)*A007948(n) + 1.
%F A097378 From _Amiram Eldar_, Feb 01 2024: (Start)
%F A097378 b(n) = a(n) - 1 is multiplicative with b(p^e) = p^(1 + min(e, 2)).
%F A097378 Dirichlet g.f.: zeta(s) * (1 + Product_{p prime} (1 + 1/p^(s-2) - 1/p^s + 1/p^(2*s-3) - 1/p^(2*s-2)).
%F A097378 Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = zeta(3) * Product_{p prime} (1 - 1/p^2 - 1/p^4 + 1/p^5) = 0.69256837284462414024... . (End)
%t A097378 f[p_, e_] := p^(1 + Min[e, 2]); a[1] = 2; a[n_] := 1 + Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Feb 01 2024 *)
%o A097378 (PARI) a(n) = {my(f = factor(n)); 1 + prod(i = 1, #f~, f[i, 1]^(1 + min(f[i, 2], 2)));} \\ _Amiram Eldar_, Feb 01 2024
%Y A097378 Cf. A002117, A004709, A005117, A007947, A007948, A097381.
%K A097378 nonn
%O A097378 1,1
%A A097378 _Reinhard Zumkeller_, Aug 11 2004