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A291502
The arithmetic function uhat(n,1,8).
0
-55, -55, -55, -55, -55, -55, -55, -55, -55, -60, -66, -72, -78, -84, -90, -96, -102, -108, -114, -120, -126, -132, -138, -144, -150, -156, -162, -168, -174, -180, -186, -192, -198, -204, -210, -216, -222, -228, -234, -240, -246, -252, -258, -264, -270, -276, -282, -288, -294, -300, -306, -312, -318, -324, -330, -336, -342, -348, -354, -360, -366, -372, -378, -384, -390, -396, -402, -408, -414, -420
OFFSET
1,1
LINKS
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, 8], {n, 1, 70}]
KEYWORD
sign
AUTHOR
Robert Price, Aug 24 2017
STATUS
approved