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 A340286 Number of partitions of n into 3 parts such that at least two parts share a common factor > 1. 0
 0, 0, 0, 0, 1, 1, 3, 2, 5, 4, 8, 5, 12, 8, 15, 13, 20, 12, 26, 17, 30, 25, 37, 22, 45, 33, 50, 39, 60, 32, 71, 50, 75, 58, 86, 54, 100, 71, 104, 79, 122, 68, 136, 95, 138, 112, 159, 92, 175, 119, 181, 140, 203, 116, 217, 157, 225, 176, 251, 133, 274, 195, 273, 212, 300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 LINKS FORMULA a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1 - [gcd(k,i) * gcd(k,n-i-k) * gcd(i,n-i-k) = 1]), where [ ] is the Iverson bracket. MATHEMATICA Table[Sum[Sum[1 - Floor[1/GCD[k, i]]*Floor[1/GCD[k, n - i - k]]* Floor[1/GCD[i, n - i - k]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 80}] CROSSREFS Cf. A307719. Sequence in context: A143527 A284153 A266794 * A194078 A169752 A095720 Adjacent sequences:  A340283 A340284 A340285 * A340287 A340288 A340289 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Jan 03 2021 STATUS approved

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Last modified January 25 10:12 EST 2022. Contains 350565 sequences. (Running on oeis4.)