A291330 The arithmetic function v_4(n,1).

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

Offset

2,2

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,4) = n - A109008(n). - Ridouane Oudra, Dec 15 2024

Sum_{n>=5} (-1)^n/a(n) = (1 - log(2))/2. - Amiram Eldar, Jan 15 2025

Maple

seq(n-gcd(n, 4), 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[4, n, 1], {n, 2, 70}]

Prog

(PARI) /* Adapted from Mathematica program */
v(g, n, h) = my(d=divisors(n)); for(k=1, #d, d[k]=floor(((d[k]-1-gcd(d[k], g))/h) + 1)*n/d[k]); vecmax(d)
a(n) = v(4, n, 1) \\ Felix Fröhlich, Aug 22 2017

Crossrefs

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

Cf. A109008.

Sequence in context: A378643 A166085 A129760 * A360133 A057377 A145811

Adjacent sequences: A291327 A291328 A291329 * A291331 A291332 A291333

Keyword

nonn

Author

Robert Price, Aug 22 2017

Status

approved