A176095 a(n) = n - phi(2*n), where phi() is the Euler totient A000010().

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

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

Cf. A000010, A000040, A051953, A062570.

Sequence in context: A022336 A019586 A257962 * A295508 A260672 A063942

Adjacent sequences: A176092 A176093 A176094 * A176096 A176097 A176098

Keyword

nonn,easy

Author

Michel Lagneau, Apr 08 2010

Extensions

Offset corrected; entry corrected and edited by Michel Lagneau, Apr 25 2010

Status

approved