A292769 Partial sums of A051612.

0, 2, 4, 9, 11, 21, 23, 34, 41, 55, 57, 81, 83, 101, 117, 140, 142, 175, 177, 211, 231, 257, 259, 311, 322, 352, 374, 418, 420, 484, 486, 533, 561, 599, 623, 702, 704, 746, 778, 852, 854, 938, 940, 1004, 1058, 1108, 1110, 1218, 1233, 1306, 1346, 1420, 1422, 1524, 1556, 1652, 1696, 1758, 1760, 1912

Offset

1,2

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Formula

G.f.: (1/(1 - x))*Sum_{k>=1} (1 - mu(k))*x^k/(1 - x^k)^2. - Ilya Gutkovskiy, Sep 28 2017

a(n) ~ c * n^2 + O(n*log(n)), where c = Pi^2/12 - 3/Pi^2 = 0.518503... . - Amiram Eldar, Oct 27 2022

Mathematica

Accumulate[Table[DivisorSigma[1, n] - EulerPhi[n], {n, 1, 50}]] (* Amiram Eldar, Oct 27 2022 *)

Prog

(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

Crossrefs

Cf. A000010, A000203, A051612.

Sequence in context: A093859 A266257 A115905 * A307997 A372686 A372517

Adjacent sequences: A292766 A292767 A292768 * A292770 A292771 A292772

Keyword

nonn

Author

N. J. A. Sloane, Sep 28 2017

Status

approved