OFFSET
1,2
COMMENTS
For Mersenne primes and also for certain composites the values of this function are powers of 2.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
FORMULA
a(2^k) = 3*2^(k-1).
Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = 1 - 3/Pi^2 = 0.696036... . - Amiram Eldar, Dec 16 2023
EXAMPLE
a(127) = 254 - 126 = 128.
a(80) = 160 - 32 = 128.
MATHEMATICA
a[n_] := 2*n - EulerPhi[n]; Array[a, 60] (* Amiram Eldar, Dec 16 2023 *)
PROG
(PARI) a(n) = 2*n - eulerphi(n); \\ Michel Marcus, Dec 19 2013
(Magma) [2*n - EulerPhi(n): n in [1..100]]; // G. C. Greubel, Feb 12 2024
(SageMath) [2*n - euler_phi(n) for n in range(1, 101)] # G. C. Greubel, Feb 12 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Feb 29 2000
EXTENSIONS
Name amended with formula by Antti Karttunen, Nov 15 2021
STATUS
approved