%I #4 Aug 24 2017 20:58:15
%S -41,-41,-41,-41,-41,-41,-41,-41,-45,-50,-55,-60,-65,-70,-75,-80,-85,
%T -90,-95,-100,-105,-110,-115,-120,-125,-130,-135,-140,-145,-150,-155,
%U -160,-165,-170,-175,-180,-185,-190,-195,-200,-205,-210,-215,-220,-225,-230,-235,-240,-245,-250,-255,-260,-265,-270,-275,-280,-285,-290,-295,-300,-305,-310,-315,-320,-325,-330,-335,-340,-345,-350
%N The arithmetic function uhat(n,1,7).
%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, 7], {n, 1, 70}]
%Y Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.
%K sign
%O 1,1
%A _Robert Price_, Aug 24 2017
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