A291306 The arithmetic function v_6(n,1).

0, 0, 2, 4, 0, 6, 6, 6, 8, 10, 6, 12, 12, 12, 14, 16, 12, 18, 18, 18, 20, 22, 18, 24, 24, 24, 26, 28, 24, 30, 30, 30, 32, 34, 30, 36, 36, 36, 38, 40, 36, 42, 42, 42, 44, 46, 42, 48, 48, 48, 50, 52, 48, 54, 54, 54, 56, 58, 54, 60, 60, 60, 62, 64, 60, 66, 66, 66, 68

Offset: 2

Author

Robert Price, Aug 21 2017

Keywords

• nonn

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.

Crossrefs

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

Cf. A089128.

Programs

Maple

seq(n-gcd(n,6), n=2..100); # Ridouane Oudra, Dec 15 2024

Mathematica

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

Formula

a(n) = n - gcd(n,6) = n - A089128(n). - Ridouane Oudra, Dec 15 2024

Sum_{n>=7} (-1)^n/a(n) = Pi/(6*sqrt(3)) - 1/4. - Amiram Eldar, Jan 15 2025