A291271 The arithmetic function v_4(n,2).
0, 1, 0, 2, 2, 3, 2, 4, 4, 5, 4, 6, 6, 7, 6, 8, 8, 9, 8, 10, 10, 11, 10, 12, 12, 13, 12, 14, 14, 15, 14, 16, 16, 17, 16, 18, 18, 19, 18, 20, 20, 21, 20, 22, 22, 23, 22, 24, 24, 25, 24, 26, 26, 27, 26, 28, 28, 29, 28, 30, 30, 31, 30, 32, 32, 33, 32, 34, 34
Offset: 2
Keywords
References
- J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).
Links
- Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], May 2017. See Table in Section 1.6.1.
Programs
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Maple
seq((n-gcd(n,4))/2, n=2..80); # Ridouane Oudra, Dec 28 2024
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Mathematica
v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[4, n, 2], {n, 2, 70}]
Formula
Conjecture: a(n) = (n-2-cos(n*Pi)-cos(n*Pi/2))/2. - Wesley Ivan Hurt, Oct 02 2017
a(n) = (n-gcd(n,4))/2 = A291330(n)/2. - Ridouane Oudra, Dec 28 2024
Sum_{n>=5} (-1)^n/a(n) = 1 - log(2) (A244009). - Amiram Eldar, Jan 15 2025
a(2)=a(4)=0, a(3)=1, a(5)=a(6)=2, a(2n+5)=n+2, a(4n+4)=2n, a(4n+6)=2n+2. - Jamil Silva, Mar 29 2025
Comments