A291581 The arithmetic function uhat(n,8,4).

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, 14, 17, 10, 17, 8, 11, 16, 14, 9, 17, 16, 13, 8, 17, 14, 17, 11, 9, 16, 17, 8, 14, 10, 17, 13, 17, 9, 11, 8, 17, 16, 17, 10, 17, 16, 9, 8, 13, 11, 17, 14, 17, 10

Offset

1,2

Links

Table of n, a(n) for n=1..70.

Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], May 2017. See Table in Section 1.6.4.

Mathematica

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}]

Crossrefs

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

Sequence in context: A216455 A338782 A291580 * A058035 A366994 A365683

Adjacent sequences: A291578 A291579 A291580 * A291582 A291583 A291584

Keyword

nonn

Author

Robert Price, Aug 26 2017

Status

approved