A290636 - OEIS

%I #20 Aug 16 2017 23:43:58

%S 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,

%T 9,17,10,18,9,19,9,20,10,21,11,22,11,23,12,24,14,25,12,26,13,27,15,28,

%U 15,29,15,30,15,31,18,32,16,33,17,34,18,35

%N The arithmetic function v_3(n,4).

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

%H Robert Israel, <a href="/A290636/b290636.txt">Table of n, a(n) for n = 2..10000</a>

%H Bela Bajnok, <a href="https://arxiv.org/abs/1705.07444">Additive Combinatorics: A Menu of Research Problems</a>, arXiv:1705.07444 [math.NT], May 2017. See Table in Section 1.6.1.

%F For n >= 3, f(prime(n)) = A024698(n-1). - _Robert Israel_, Aug 16 2017

%p f:= n -> max(map(t -> (floor((t - 1 - igcd(t, 3))/4) + 1)*n/t, numtheory:-divisors(n))):

%p map(f, [$2..100]); # _Robert Israel_, Aug 16 2017

%t 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}]

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

%Y Cf. A289435 - A289441.

%Y Cf. A024698.

%K nonn

%O 2,3

%A _Robert Price_, Aug 13 2017