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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

(list; graph; refs; listen; history; text; internal format)

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;