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 A090029 Number of distinct lines through the origin in 7-dimensional cube of side length n. 12
 0, 127, 2059, 16129, 75811, 277495, 804973, 2078455, 4702531, 9905365, 19188793, 35533303, 61846723, 104511583, 168681913, 266042113, 405259513, 607140745, 883046011, 1269174145, 1780715833, 2472697501, 3366818491, 4548464341 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equivalently, lattice points where the GCD of all coordinates = 1. LINKS FORMULA a(n) = A090030(7, n). a(n) = (n+1)^7 - 1 - Sum_{j=2..n+1} a(floor(n/j)). - Chai Wah Wu, Mar 30 2021 EXAMPLE a(2) = 2059 because the 2059 points with at least one coordinate=2 all make distinct lines and the remaining 127 points and the origin are on those lines. MATHEMATICA aux[n_, k_] := If[k == 0, 0, (k + 1)^n - k^n - Sum[aux[n, Divisors[k][[i]]], {i, 1, Length[Divisors[k]] - 1}]]; lines[n_, k_] := (k + 1)^n - Sum[Floor[k/i - 1]*aux[n, i], {i, 1, Floor[k/2]}] - 1; Table[lines[7, k], {k, 0, 40}] PROG (Python) from functools import lru_cache @lru_cache(maxsize=None) def A090029(n):     if n == 0:         return 0     c, j = 1, 2     k1 = n//j     while k1 > 1:         j2 = n//k1 + 1         c += (j2-j)*A090029(k1)         j, k1 = j2, n//j2     return (n+1)**7-c+127*(j-n-1) # Chai Wah Wu, Mar 30 2021 CROSSREFS Cf. A000225, A001047, A060867, A090020, A090021, A090022, A090023, A090024 are for n dimensions with side length 1, 2, 3, 4, 5, 6, 7, 8, respectively. A049691, A090025, A090026, A090027, A090028, A090029 are this sequence for 2, 3, 4, 5, 6, 7 dimensions. A090030 is the table for n dimensions, side length k. Sequence in context: A228263 A228222 A022523 * A152726 A069092 A024005 Adjacent sequences:  A090026 A090027 A090028 * A090030 A090031 A090032 KEYWORD nonn AUTHOR Joshua Zucker, Nov 25 2003 STATUS approved

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Last modified June 22 15:08 EDT 2021. Contains 345383 sequences. (Running on oeis4.)