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A337601
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Number of unordered triples of positive integers summing to n whose set of distinct parts is pairwise coprime, where a singleton is not considered coprime unless it is (1).
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15
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0, 0, 0, 1, 1, 2, 2, 3, 4, 4, 5, 6, 8, 7, 10, 7, 11, 11, 17, 12, 19, 12, 19, 17, 29, 16, 28, 19, 31, 23, 46, 23, 42, 25, 45, 27, 59, 31, 57, 34, 61, 37, 84, 38, 75, 42, 74, 47, 107, 45, 98, 51, 96, 56, 135, 54, 115, 63, 117, 67, 174, 65, 139, 75, 144, 75, 194
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OFFSET
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0,6
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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The a(3) = 1 through a(14) = 10 partitions (A = 10, B = 11, C = 12):
111 211 221 321 322 332 441 433 443 543 544 554
311 411 331 431 522 532 533 552 553 743
511 521 531 541 551 651 661 752
611 711 721 722 732 733 761
811 731 741 751 833
911 831 922 851
921 B11 941
A11 A31
B21
C11
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n, {3}], CoprimeQ@@Union[#]&]], {n, 0, 100}]
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CROSSREFS
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A304709 counts these partitions of any length.
A307719 is the strict case except for any number of 1's.
A337600 considers singletons to be coprime.
A000217 counts 3-part compositions.
A000837 counts relatively prime partitions.
A023023 counts relatively prime 3-part partitions.
A051424 counts pairwise coprime or singleton partitions.
A101268 counts pairwise coprime or singleton compositions.
A305713 counts pairwise coprime strict partitions.
A327516 counts pairwise coprime partitions.
A333227 ranks pairwise coprime compositions.
A333228 ranks compositions whose distinct parts are pairwise coprime.
A337461 counts pairwise coprime 3-part compositions.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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