A291572 The arithmetic function uhat(n,6,3).

1, 2, 3, 4, 5, 6, 7, 8, 8, 10, 10, 6, 10, 7, 8, 8, 10, 6, 10, 10, 7, 10, 10, 6, 10, 10, 8, 7, 10, 6, 10, 8, 8, 10, 7, 6, 10, 10, 8, 8, 10, 6, 10, 10, 8, 10, 10, 6, 7, 10, 8, 10, 10, 6, 10, 7, 8, 10, 10, 6, 10, 10, 7, 8, 10, 6, 10, 10, 8, 7

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, 6, 3], {n, 1, 70}]

Crossrefs

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

Sequence in context: A160755 A017873 A274016 * A265541 A128557 A376915

Adjacent sequences: A291569 A291570 A291571 * A291573 A291574 A291575

Keyword

nonn

Author

Robert Price, Aug 26 2017

Status

approved