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A291499 The arithmetic function uhat(n,1,5). 0
-19, -19, -19, -19, -19, -19, -21, -24, -27, -30, -33, -36, -39, -42, -45, -48, -51, -54, -57, -60, -63, -66, -69, -72, -75, -78, -81, -84, -87, -90, -93, -96, -99, -102, -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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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, 1, 5], {n, 1, 70}]

CROSSREFS

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

Sequence in context: A291475 A057430 A010858 * A168525 A272897 A040343

Adjacent sequences:  A291496 A291497 A291498 * A291500 A291501 A291502

KEYWORD

sign

AUTHOR

Robert Price, Aug 24 2017

STATUS

approved

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Last modified January 20 19:53 EST 2020. Contains 331096 sequences. (Running on oeis4.)