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

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, 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, 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

Offset: 1

Author

Labos Elemer, Sep 03 2004

Keywords

• nonn

Examples

			a(1) = 1 - 1 = 0.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

Table[DivisorSum[n, # &, CoprimeQ[#, n/#] &] - EulerPhi@ n, {n, 120}] (* Michael De Vlieger, Mar 01 2017 *)

PARI

a(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - eulerphi(n); \\ Michel Marcus, Feb 25 2014

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

Formula

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

a(A000040(k)) = 2.

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

Extensions

Edited by R. J. Mathar, Mar 02 2009