A324048 a(n) = A000203(n) - A083254(n) = n + sigma(n) - 2*phi(n).

0, 3, 3, 7, 3, 14, 3, 15, 10, 20, 3, 32, 3, 26, 23, 31, 3, 45, 3, 46, 29, 38, 3, 68, 16, 44, 31, 60, 3, 86, 3, 63, 41, 56, 35, 103, 3, 62, 47, 98, 3, 114, 3, 88, 75, 74, 3, 140, 22, 103, 59, 102, 3, 138, 47, 128, 65, 92, 3, 196, 3, 98, 95, 127, 53, 170, 3, 130, 77, 166, 3, 219, 3, 116, 119, 144, 53, 198, 3, 202, 94, 128, 3

Offset: 1

Author

Antti Karttunen, Feb 13 2019

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000010, A000203, A001065, A051709, A051612, A051953, A083254, A297159.

Programs

Mathematica

a[n_] := n + DivisorSigma[1, n] - 2 * EulerPhi[n]; Array[a, 100] (* Amiram Eldar, Dec 04 2023 *)

PARI

A083254(n) = (2*eulerphi(n)-n);
A324048(n) = (sigma(n) - A083254(n));

PARI

a(n) = {my(f = factor(n)); n + sigma(f) - 2*eulerphi(f);} \\ Amiram Eldar, Dec 04 2023

Formula

a(n) = A000203(n) - A083254(n) = n + A000203(n) - 2*A000010(n).

a(n) = A051612(n) + A051953(n).

a(n) = A297159(n) + 2*A001065(n).

Sum_{k=1..n} a(k) = (Pi^2/12 - 6/Pi^2 + 1/2) * n^2 + O(n*log(n)). - Amiram Eldar, Dec 04 2023