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

Author

N. J. A. Sloane, Sep 28 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A000010, A000203, A051612.

Programs

Mathematica

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

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

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