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 A343100 Number of partitions of n into 3 parts, at least 2 of which are coprime. 0
 0, 0, 1, 1, 2, 2, 4, 4, 6, 6, 10, 8, 14, 12, 16, 16, 24, 18, 30, 24, 32, 30, 44, 32, 50, 42, 54, 48, 70, 48, 79, 64, 80, 72, 96, 72, 113, 90, 112, 96, 138, 96, 153, 120, 144, 132, 182, 128, 195, 150, 192, 168, 232, 162, 239, 192, 240, 210, 287, 192, 305, 240, 288, 256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Table of n, a(n) for n=1..64. Index entries for sequences related to partitions FORMULA a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} sign(floor(1/gcd(i, j)) + floor(1/gcd(i, n-i-j)) + floor(1/gcd(j, n-i-j))). EXAMPLE a(12) = 8; [10,1,1], [9,2,1], [8,3,1], [7,4,1], [7,3,2], [6,5,1], [5,5,2], [5,4,3]. MATHEMATICA Table[Sum[Sum[Sign[Floor[1/GCD[i, j]] + Floor[1/GCD[i, n - i - j]] + Floor[1/GCD[j, n - i - j]]], {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}] CROSSREFS Cf. A023023, A069905. Sequence in context: A029009 A340280 A340279 * A023023 A184157 A008643 Adjacent sequences: A343097 A343098 A343099 * A343101 A343102 A343103 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Apr 05 2021 STATUS approved

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Last modified September 16 11:09 EDT 2024. Contains 375965 sequences. (Running on oeis4.)