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%I #4 Aug 27 2017 12:52:27
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,8,17,9,17,10,14,11,17,8,17,13,9,
%T 14,17,10,17,8,11,16,14,9,17,16,13,8,17,14,17,11,9,16,17,8,14,10,17,
%U 13,17,9,11,8,17,16,17,10,17,16,9,8,13,11,17,14,17,10
%N The arithmetic function uhat(n,8,4).
%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, 8, 4], {n, 1, 70}]
%Y Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.
%K nonn
%O 1,2
%A _Robert Price_, Aug 26 2017
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