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 A073355 #49 Mar 25 2025 17:10:48
%S A073355 1,3,6,8,13,19,26,28,31,41,52,58,71,85,100,102,119,125,144,154,175,
%T A073355 197,220,226,231,257,260,274,303,333,364,366,399,433,468,474,511,549,
%U A073355 588,598,639,681,724,746,761,807,854,860,867,877,928,954,1007,1013,1068
%N A073355 Sum of squarefree kernels of numbers <= n.
%D A073355 Gérald Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Cours spécialisé, collection SMF, 1995, p. 55.
%H A073355 Vaclav Kotesovec, <a href="/A073355/b073355.txt">Table of n, a(n) for n = 1..10000</a>
%H A073355 Eckford Cohen, <a href="https://doi.org/10.1090/S0002-9947-1964-0166181-5">Some asymptotic formulas in the theory of numbers</a>, Trans. Amer. Math. Soc. 112 (1964) 214-227.
%H A073355 Vaclav Kotesovec, <a href="/A073355/a073355.jpg">Graph a(n)/n^2 (1000000 terms)</a>.
%F A073355 a(n) = (1/2)*C*n^2 + O(n^(3/2)) where C = Product_{p prime} (1 - 1/(p*(p+1))) = 0.7044... (see A065463). - _Benoit Cloitre_, Jan 31 2003
%F A073355 G.f.: (1/(1 - x))*Sum_{k>=1} phi(k)*mu(k)^2*x^k/(1 - x^k). - _Ilya Gutkovskiy_, Apr 15 2017
%F A073355 a(n) = Sum_{i=1..n} phi(i)*mu(i)^2*floor(n/i). - _Ridouane Oudra_, Oct 17 2019
%F A073355 a(n) = Sum_{k=1..n} rad(k). - _Wesley Ivan Hurt_, Jun 12 2021
%p A073355 with(numtheory): A073355 := n -> add(ilcm(op(factorset(k))), k = 1 .. n): seq(A073355(i), i = 1 .. 52); # _Peter Luschny_, Jun 23 2011
%t A073355 Accumulate[Table[Last[Select[Divisors[n], SquareFreeQ]], {n, 100}]] (* _Vaclav Kotesovec_, Oct 06 2016 *)
%t A073355 Drop[CoefficientList[Series[(1/(1 - x))*Sum[EulerPhi[k] MoebiusMu[k]^2*x^k/(1 - x^k), {k, 100}], {x, 0, 100}], x], 1] (* _Indranil Ghosh_, Apr 16 2017 *)
%t A073355 rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; Accumulate[Array[rad, 100]] (* _Amiram Eldar_, Mar 25 2025 *)
%o A073355 (PARI) print1(s=1);for(n=2,99,t=factor(n)[,1];print1(", ",s+=prod(i=1,#t,t[i]))) \\ _Charles R Greathouse IV_, Jun 24 2011
%Y A073355 Partial sums of A007947.
%Y A073355 Cf. A000217, A065463, A073356.
%K A073355 nonn,easy
%O A073355 1,2
%A A073355 _Reinhard Zumkeller_, Jul 29 2002