A291307 The arithmetic function v_6(n,2).

0, 0, 1, 2, 0, 3, 3, 3, 4, 5, 3, 6, 6, 6, 7, 8, 6, 9, 9, 9, 10, 11, 9, 12, 12, 12, 13, 14, 12, 15, 15, 15, 16, 17, 15, 18, 18, 18, 19, 20, 18, 21, 21, 21, 22, 23, 21, 24, 24, 24, 25, 26, 24, 27, 27, 27, 28, 29, 27, 30, 30, 30, 31, 32, 30, 33, 33, 33, 34

Offset

2,4

References

J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).

Links

Table of n, a(n) for n=2..70.

Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], May 2017. See Table in Section 1.6.1.

Formula

a(n) = (n-gcd(n,6))/2 = A291306(n)/2. - Ridouane Oudra, Jan 09 2025

Sum_{n>=7} (-1)^n/a(n) = Pi/(3*sqrt(3)) - 1/2. - Amiram Eldar, Jan 15 2025

Maple

seq((n-gcd(n, 6))/2, n=2..80); # Ridouane Oudra, Jan 09 2025

Mathematica

v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[6, n, 2], {n, 2, 70}]

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Cf. A291306.

Sequence in context: A329098 A038073 A283981 * A239313 A046667 A108407

Adjacent sequences: A291304 A291305 A291306 * A291308 A291309 A291310

Keyword

nonn

Author

Robert Price, Aug 21 2017

Status

approved