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A291306
The arithmetic function v_6(n,1).
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
2,3
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.
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
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}]
KEYWORD
nonn,changed
AUTHOR
Robert Price, Aug 21 2017
STATUS
approved