A290636 The arithmetic function v_3(n,4).

1, 0, 2, 1, 3, 2, 4, 2, 5, 3, 6, 3, 7, 3, 8, 4, 9, 5, 10, 6, 11, 6, 12, 6, 13, 6, 14, 7, 15, 8, 16, 9, 17, 10, 18, 9, 19, 9, 20, 10, 21, 11, 22, 11, 23, 12, 24, 14, 25, 12, 26, 13, 27, 15, 28, 15, 29, 15, 30, 15, 31, 18, 32, 16, 33, 17, 34, 18, 35

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

Robert Israel, Table of n, a(n) for n = 2..10000

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

Formula

For n >= 3, f(prime(n)) = A024698(n-1). - Robert Israel, Aug 16 2017

Maple

f:= n -> max(map(t -> (floor((t - 1 - igcd(t, 3))/4) + 1)*n/t, numtheory:-divisors(n))):
map(f, [$2..100]); # Robert Israel, Aug 16 2017

Mathematica

v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[3, n, 4], {n, 2, 70}]

Crossrefs

Cf. A211316 (equals v_1(n,3)).

Cf. A289435 - A289441.

Cf. A024698.

Sequence in context: A302604 A214270 A289440 * A106466 A130722 A308307

Adjacent sequences: A290633 A290634 A290635 * A290637 A290638 A290639

Keyword

nonn

Author

Robert Price, Aug 13 2017

Status

approved