A291502 - OEIS

%I #4 Aug 24 2017 20:58:23

%S -55,-55,-55,-55,-55,-55,-55,-55,-55,-60,-66,-72,-78,-84,-90,-96,-102,

%T -108,-114,-120,-126,-132,-138,-144,-150,-156,-162,-168,-174,-180,

%U -186,-192,-198,-204,-210,-216,-222,-228,-234,-240,-246,-252,-258,-264,-270,-276,-282,-288,-294,-300,-306,-312,-318,-324,-330,-336,-342,-348,-354,-360,-366,-372,-378,-384,-390,-396,-402,-408,-414,-420

%N The arithmetic function uhat(n,1,8).

%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, 1, 8], {n, 1, 70}]

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

%K sign

%O 1,1

%A _Robert Price_, Aug 24 2017