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A338332
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Number of relatively prime 3-part integer partitions of n with no 1's.
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3
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0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 5, 3, 8, 6, 9, 9, 16, 10, 21, 15, 22, 20, 33, 21, 38, 30, 41, 35, 56, 34, 65, 49, 64, 56, 79, 55, 96, 72, 93, 77, 120, 76, 133, 99, 122, 110, 161, 105, 172, 126, 167, 143, 208, 136, 213, 165, 212, 182, 261, 163, 280, 210, 257
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OFFSET
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0,10
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COMMENTS
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The Heinz numbers of these partitions are the intersection of A005408 (no 1's), A014612 (length 3), and A289509 (relatively prime).
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LINKS
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EXAMPLE
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The a(7) = 1 through a(17) = 16 triples (A = 10, B = 11, C = 12, D = 13):
322 332 432 433 443 543 544 554 654 655 665
522 532 533 552 553 653 744 754 755
542 732 643 743 753 763 764
632 652 752 762 772 773
722 733 833 843 853 854
742 932 852 943 863
832 942 952 872
922 A32 A33 944
B22 B32 953
962
A43
A52
B33
B42
C32
D22
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n, {3}], !MemberQ[#, 1]&&GCD@@#==1&]], {n, 0, 30}]
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CROSSREFS
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A001399(n-6) does not require relative primality.
A284825 counts the case that is also pairwise non-coprime.
A302698 counts these partitions of any length.
A337563 is the pairwise coprime instead of relatively prime version.
A008284 counts partitions by sum and length.
Cf. A000010, A000741, A023022, A078374, A082024, A101271, A307719, A337450, A337599, A337600, A337601.
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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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