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 A363278 Total number of parts coprime to n in the partitions of n into 3 parts. 7
 0, 0, 3, 2, 6, 3, 12, 8, 15, 10, 30, 12, 42, 21, 32, 32, 72, 27, 90, 40, 66, 55, 132, 48, 130, 78, 126, 84, 210, 60, 240, 128, 170, 136, 216, 108, 342, 171, 240, 160, 420, 126, 462, 220, 276, 253, 552, 192, 525, 250, 416, 312, 702, 243, 560, 336, 522, 406, 870, 240, 930, 465 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..62. Index entries for sequences related to partitions FORMULA a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} ([gcd(n,n-i-j) = 1] + [gcd(n,i) = 1] + [gcd(n,j) = 1]), where [ ] is the Iverson Bracket. EXAMPLE The partitions of 5 into 3 parts are: 3+1+1 and 2+2+1. 5 is coprime to 1, 2 and 3. Since there are 6 total parts in the partitions of 5 that are coprime to 5, a(5) = 6. MATHEMATICA Table[Sum[Sum[KroneckerDelta[GCD[n, n - i - j], 1] + KroneckerDelta[GCD[n, j], 1] + KroneckerDelta[GCD[n, i], 1], {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}] CROSSREFS For similar sequences into k parts for k = 2..10, see: A000010(n>2) (k=2), this sequence (k=3), A363322 (k=4), A363323 (k=5), A363324 (k=6), A363325 (k=7), A363326 (k=8), A363327 (k=9), A363328 (k=10). Sequence in context: A064455 A141619 A270143 * A065021 A048652 A195345 Adjacent sequences: A363275 A363276 A363277 * A363279 A363280 A363281 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, May 25 2023 STATUS approved

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Last modified September 13 07:28 EDT 2024. Contains 375866 sequences. (Running on oeis4.)