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 A340282 Number of partitions of n into 3 parts such that the largest part is relatively prime to at least one other part. 1
 0, 0, 1, 1, 2, 2, 4, 4, 6, 6, 9, 8, 13, 12, 16, 16, 22, 18, 28, 24, 31, 30, 38, 32, 46, 41, 52, 47, 63, 48, 72, 63, 78, 70, 89, 72, 101, 88, 107, 95, 125, 96, 139, 118, 141, 131, 164, 128, 180, 148, 184, 166, 209, 161, 222, 189, 228, 205, 258, 192, 277, 236, 279, 250, 310 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Table of n, a(n) for n=1..65. Index entries for sequences related to partitions FORMULA a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor(1/gcd(n-i-k,k)) + floor(1/gcd(n-i-k,i))). MATHEMATICA Table[Sum[Sum[Sign[Floor[1/GCD[n - i - k, k]] + Floor[1/GCD[n - i - k, i]]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 80}] lppQ[{a_, b_, c_}]:=Total[Boole[{CoprimeQ[c, a], CoprimeQ[b, a]}]]>0; Table[Length[ Select[ IntegerPartitions[n, {3}], lppQ]], {n, 70}] (* Harvey P. Dale, May 08 2022 *) CROSSREFS Cf. A340279, A340280. Sequence in context: A238132 A278296 A332305 * A008642 A001364 A029010 Adjacent sequences: A340279 A340280 A340281 * A340283 A340284 A340285 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Jan 02 2021 STATUS approved

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Last modified September 12 05:07 EDT 2024. Contains 375842 sequences. (Running on oeis4.)