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A176095
a(n) = n - phi(2*n), where phi() is the Euler totient A000010().
2
0, 0, 1, 0, 1, 2, 1, 0, 3, 2, 1, 4, 1, 2, 7, 0, 1, 6, 1, 4, 9, 2, 1, 8, 5, 2, 9, 4, 1, 14, 1, 0, 13, 2, 11, 12, 1, 2, 15, 8, 1, 18, 1, 4, 21, 2, 1, 16, 7, 10, 19, 4, 1, 18, 15, 8, 21, 2, 1, 28, 1, 2, 27, 0, 17, 26, 1, 4, 25, 22, 1, 24, 1, 2, 35, 4, 17, 30, 1, 16, 27, 2, 1, 36, 21, 2, 31, 8, 1, 42, 19
OFFSET
1,6
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
Tom M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 24.
FORMULA
a(n) = n - A062570(n).
a(2^k) = 0, k >= 0. - Michel Lagneau, Dec 17 2010
a(A000040(k)) = 1, k >= 2. - Michel Lagneau, Dec 17 2010, corrected by Antti Karttunen, May 19 2021
a(2^m*A000040(k)) = 2^m, m >= 1, k >= 2. - Michel Lagneau, Dec 17 2010
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1 - 8/Pi^2 = 0.1894305... . - Amiram Eldar, Dec 21 2023
EXAMPLE
a(1) = 1 - phi(2) = 0;
a(2) = 2 - phi(2*2) = 2 - 2 = 0;
a(3) = 3 - phi(2*3) = 3 - 2 = 1;
If n = (2^m)*p, with m = 3 and p = 7, then n = 2^3 * 7 = 56, and a(56) = 2^3 = 8.
MAPLE
A176095 := proc(n)
n-numtheory[phi](2*n) ;
end proc:
seq(A176095(n), n=1..60) ;
MATHEMATICA
Table[n-EulerPhi[2n], {n, 0, 100}] (* Harvey P. Dale, Jul 24 2011 *)
PROG
(PARI) A176095(n) = (n-eulerphi(n+n)); \\ Antti Karttunen, May 19 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michel Lagneau, Apr 08 2010
EXTENSIONS
Offset corrected; entry corrected and edited by Michel Lagneau, Apr 25 2010
STATUS
approved