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The arithmetic function uhat(n,3,7), negated.
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%I #8 Sep 03 2017 17:16:40

%S 27,27,27,27,27,27,27,27,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,

%T 72,75,78,81,84,87,90,93,96,99,102,105,108,111,114,117,120,123,126,

%U 129,132,135,138,141,144,147,150,153,156,159,162,165,168,171,174,177,180,183,186,189,192,195,198,201,204,207,210

%N The arithmetic function uhat(n,3,7), negated.

%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, 3, 7], {n, 1, 70}]

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

%K nonn

%O 1,1

%A _Robert Price_, Aug 25 2017