A209187 - OEIS

%I #25 Dec 22 2024 12:16:59

%S 1,2,3,5,5,8,7,11,10,12,11,20,13,16,17,23,17,27,19,30,23,24,23,44,26,

%T 28,31,40,29,50,31,47,35,36,37,67,37,40,41,66,41,66,43,60,57,48,47,92,

%U 50,63,53,70,53,84,57,88,59,60,59,124,61,64,77,95,67,98,67,90,71,98,71

%N Sum of divisors of n minus cototient of n.

%H Ivan Neretin, <a href="/A209187/b209187.txt">Table of n, a(n) for n = 1..10000</a>

%H PrimeFan, <a href="http://primefan.tripod.com/EsotericIntegerSequences.html">Listing of Esoteric Integer Sequences</a>.

%H PrimeFan, <a href="/A031214/a031214.pdf">Esoteric Integer Sequences</a> [Cached copy]

%F a(n) = A065387(n) - n. - _Altug Alkan_, Sep 30 2017

%F a(n) = A000203(n) - A051953(n). - _Omar E. Pol_, Sep 30 2017

%F Sum_{k=1..n} a(k) = c * n^2 / 2 + O(n*log(n)), where c = 6/Pi^2 + Pi^2/6 - 1 = 1.252861... . - _Amiram Eldar_, Dec 08 2023

%t Table[(Plus @@ Divisors[n]) - (n - EulerPhi[n]), {n, 50}]

%o (PARI) a(n) = sigma(n) + eulerphi(n) - n; \\ _Altug Alkan_, Sep 30 2017

%Y Cf. A000203, A051953, A065387.

%Y Cf. A013661, A059956.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Mar 05 2012