This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A291499 #7 Jun 11 2025 00:58:07
%S A291499 -19,-19,-19,-19,-19,-19,-21,-24,-27,-30,-33,-36,-39,-42,-45,-48,-51,
%T A291499 -54,-57,-60,-63,-66,-69,-72,-75,-78,-81,-84,-87,-90,-93,-96,-99,-102,
%U A291499 -105,-108,-111,-114,-117,-120,-123,-126,-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 A291499 The arithmetic function uhat(n,1,5).
%H A291499 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.
%F A291499 Conjectures from _Chai Wah Wu_, Jun 10 2025: (Start)
%F A291499 a(n) = 2*a(n-1) - a(n-2) for n > 8.
%F A291499 G.f.: x*(-x^7 - 2*x^6 + 19*x - 19)/(x - 1)^2. (End)
%t A291499 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, 5], {n, 1, 70}]
%Y A291499 Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.
%K A291499 sign
%O A291499 1,1
%A A291499 _Robert Price_, Aug 24 2017