A291521 - OEIS

%I #4 Aug 26 2017 08:36:08

%S -11,-12,-11,-12,-11,-12,-11,-12,-11,-12,-11,-12,-13,-14,-15,-16,-17,

%T -18,-19,-20,-21,-22,-23,-24,-25,-26,-27,-28,-29,-30,-31,-32,-33,-34,

%U -35,-36,-37,-38,-39,-40,-41,-42,-43,-44,-45,-46,-47,-48,-49,-50,-51,-52,-53,-54,-55,-56,-57,-58,-59,-60,-61,-62,-63,-64,-65,-66,-67,-68,-69,-70

%N The arithmetic function uhat(n,4,6).

%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 1.6.4.

%t delta[r_, k_, d_] := If[r < k, (k - r)*r - (d - 1), If[k < r && r < d, (d - r)*(r - k) - (d - 1), If[k == r && r == d, d - 1, 0]]] uhat[n_, m_, h_] := (dx = Divisors[n]; dmin = n; For[i = 1, i ≤ Length[dx], i++, d = dx[[i]]; k = m - d*Ceiling[m/d] + d; r = h - d*Ceiling[h/d] + d; If[h ≤ Min[k, d - 1], dmin = Min[dmin, n, (h*Ceiling[m/d] - h + 1)*d, h*m - h*h + 1], dmin = Min[dmin, n, h*m - h*h + 1 - delta[r, k, d]]]]; dmin) Table[uhat[n, 4, 6], {n, 1, 70}]

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

%K sign

%O 1,1

%A _Robert Price_, Aug 25 2017