A098189 - OEIS

%I #18 Aug 22 2023 08:00:32

%S 0,2,2,3,2,10,2,5,4,14,2,16,2,18,16,9,2,24,2,22,20,26,2,28,6,30,10,28,

%T 2,64,2,17,28,38,24,38,2,42,32,38,2,84,2,40,36,50,2,52,8,58,40,46,2,

%U 66,32,48,44,62,2,104,2,66,44,33,36,124,2,58,52,120,2,66,2,78,64,64,36,144,2

%N Sum of unitary divisors minus Euler phi: a(n) = A034448(n) - A000010(n).

%H Michael De Vlieger, <a href="/A098189/b098189.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) > A063919(n) if n > 1.

%F a(A000040(k)) = 2.

%F Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/(12*zeta(3)) - 3/Pi^2 = 0.380252... . - _Amiram Eldar_, Aug 21 2023

%e a(1) = 1 - 1 = 0.

%t Table[DivisorSum[n, # &, CoprimeQ[#, n/#] &] - EulerPhi@ n, {n, 120}] (* _Michael De Vlieger_, Mar 01 2017 *)

%o (PARI) a(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - eulerphi(n); \\ _Michel Marcus_, Feb 25 2014

%o (PARI) a(n)=my(f=factor(n)); prod(k=1, #f[, 2], f[k, 1]^f[k, 2]+1) - eulerphi(f) \\ _Charles R Greathouse IV_, Mar 01 2017

%Y Cf. A034448, A000010, A063919, A098190, A098191, A098192, A098193, A098194, A098195.

%K nonn

%O 1,2

%A _Labos Elemer_, Sep 03 2004

%E Edited by _R. J. Mathar_, Mar 02 2009