A291512 - OEIS

%I #13 Sep 12 2018 16:39:56

%S -34,-34,-34,-34,-34,-34,-34,-34,-36,-40,-44,-48,-52,-56,-60,-64,-68,

%T -72,-76,-80,-84,-88,-92,-96,-100,-104,-108,-112,-116,-120,-124,-128,

%U -132,-136,-140,-144,-148,-152,-156,-160,-164,-168,-172,-176,-180,-184,-188,-192,-196,-200,-204,-208,-212,-216,-220,-224,-228,-232,-236,-240,-244,-248,-252,-256,-260,-264,-268,-272,-276,-280

%N The arithmetic function uhat(n,2,7).

%C Appears to decrement by 4 for each successive term after a(9) = -36. - _Chai Wah Wu_, Sep 12 2018

%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, 2, 7], {n, 1, 70}]

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

%K sign

%O 1,1

%A _Robert Price_, Aug 25 2017