cp's OEIS Frontend

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.

A292769 Partial sums of A051612.

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%I A292769 #15 Oct 27 2022 07:32:12
%S A292769 0,2,4,9,11,21,23,34,41,55,57,81,83,101,117,140,142,175,177,211,231,
%T A292769 257,259,311,322,352,374,418,420,484,486,533,561,599,623,702,704,746,
%U A292769 778,852,854,938,940,1004,1058,1108,1110,1218,1233,1306,1346,1420,1422,1524,1556,1652,1696,1758,1760,1912
%N A292769 Partial sums of A051612.
%H A292769 N. J. A. Sloane, <a href="/A292769/b292769.txt">Table of n, a(n) for n = 1..10000</a>
%F A292769 G.f.: (1/(1 - x))*Sum_{k>=1} (1 - mu(k))*x^k/(1 - x^k)^2. - _Ilya Gutkovskiy_, Sep 28 2017
%F A292769 a(n) ~ c * n^2 + O(n*log(n)), where c = Pi^2/12 - 3/Pi^2 = 0.518503... . - _Amiram Eldar_, Oct 27 2022
%t A292769 Accumulate[Table[DivisorSigma[1, n] - EulerPhi[n], {n, 1, 50}]] (* _Amiram Eldar_, Oct 27 2022 *)
%o A292769 (PARI) lista(nmax) = {my(s = 0, f); for(n = 1, nmax, f = factor(n); s += sigma(f) - eulerphi(f); print1(s, ", "));} \\ _Amiram Eldar_, Oct 27 2022
%Y A292769 Cf. A000010, A000203, A051612.
%K A292769 nonn
%O A292769 1,2
%A A292769 _N. J. A. Sloane_, Sep 28 2017