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A098189 Sum of unitary divisors minus Euler phi: a(n) = A034448(n) - A000010(n).

%I A098189 #18 Aug 22 2023 08:00:32
%S A098189 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 A098189 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 A098189 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 A098189 Sum of unitary divisors minus Euler phi: a(n) = A034448(n) - A000010(n).
%H A098189 Michael De Vlieger, <a href="/A098189/b098189.txt">Table of n, a(n) for n = 1..10000</a>
%F A098189 a(n) > A063919(n) if n > 1.
%F A098189 a(A000040(k)) = 2.
%F A098189 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 A098189 a(1) = 1 - 1 = 0.
%t A098189 Table[DivisorSum[n, # &, CoprimeQ[#, n/#] &] - EulerPhi@ n, {n, 120}] (* _Michael De Vlieger_, Mar 01 2017 *)
%o A098189 (PARI) a(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - eulerphi(n); \\ _Michel Marcus_, Feb 25 2014
%o A098189 (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 A098189 Cf. A034448, A000010, A063919, A098190, A098191, A098192, A098193, A098194, A098195.
%K A098189 nonn
%O A098189 1,2
%A A098189 _Labos Elemer_, Sep 03 2004
%E A098189 Edited by _R. J. Mathar_, Mar 02 2009