A324048 - OEIS

%I #14 Dec 04 2023 01:34:10

%S 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,

%T 31,60,3,86,3,63,41,56,35,103,3,62,47,98,3,114,3,88,75,74,3,140,22,

%U 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

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

%H Antti Karttunen, <a href="/A324048/b324048.txt">Table of n, a(n) for n = 1..20000</a>

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

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

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

%F 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

%t a[n_] := n + DivisorSigma[1, n] - 2 * EulerPhi[n]; Array[a, 100] (* _Amiram Eldar_, Dec 04 2023 *)

%o (PARI)

%o A083254(n) = (2*eulerphi(n)-n);

%o A324048(n) = (sigma(n) - A083254(n));

%o (PARI) a(n) = {my(f = factor(n)); n + sigma(f) - 2*eulerphi(f);} \\ _Amiram Eldar_, Dec 04 2023

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

%K nonn,easy

%O 1,2

%A _Antti Karttunen_, Feb 13 2019