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%I #4 Aug 27 2017 12:51:00
%S -23,-23,-23,-23,-25,-24,-23,-23,-23,-25,-23,-24,-26,-28,-30,-32,-34,
%T -36,-38,-40,-42,-44,-46,-48,-50,-52,-54,-56,-58,-60,-62,-64,-66,-68,
%U -70,-72,-74,-76,-78,-80,-82,-84,-86,-88,-90,-92,-94,-96,-98,-100,-102,-104,-106,-108,-110,-112,-114,-116,-118,-120,-122,-124,-126,-128,-130,-132,-134,-136,-138,-140
%N The arithmetic function uhat(n,5,8).
%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, 5, 8], {n, 1, 70}]
%Y Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.
%K sign
%O 1,1
%A _Robert Price_, Aug 26 2017
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