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A337984
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Heinz numbers of pairwise coprime integer partitions with no 1's, where a singleton is not considered coprime.
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9
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15, 33, 35, 51, 55, 69, 77, 85, 93, 95, 119, 123, 141, 143, 145, 155, 161, 165, 177, 187, 201, 205, 209, 215, 217, 219, 221, 249, 253, 255, 265, 287, 291, 295, 309, 323, 327, 329, 335, 341, 355, 381, 385, 391, 395, 403, 407, 411, 413, 415, 437, 447, 451, 465
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OFFSET
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1,1
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COMMENTS
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The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
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LINKS
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FORMULA
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EXAMPLE
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The sequence of terms together with their prime indices begins:
15: {2,3} 155: {3,11} 265: {3,16}
33: {2,5} 161: {4,9} 287: {4,13}
35: {3,4} 165: {2,3,5} 291: {2,25}
51: {2,7} 177: {2,17} 295: {3,17}
55: {3,5} 187: {5,7} 309: {2,27}
69: {2,9} 201: {2,19} 323: {7,8}
77: {4,5} 205: {3,13} 327: {2,29}
85: {3,7} 209: {5,8} 329: {4,15}
93: {2,11} 215: {3,14} 335: {3,19}
95: {3,8} 217: {4,11} 341: {5,11}
119: {4,7} 219: {2,21} 355: {3,20}
123: {2,13} 221: {6,7} 381: {2,31}
141: {2,15} 249: {2,23} 385: {3,4,5}
143: {5,6} 253: {5,9} 391: {7,9}
145: {3,10} 255: {2,3,7} 395: {3,22}
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MATHEMATICA
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Select[Range[1, 100, 2], SquareFreeQ[#]&&CoprimeQ@@PrimePi/@First/@FactorInteger[#]&]
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CROSSREFS
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A302568 considers singletons to be coprime.
A337694 is the pairwise non-coprime instead of pairwise coprime version.
A007359 counts partitions into singleton or pairwise coprime parts with no 1's
A101268 counts pairwise coprime or singleton compositions, ranked by A335235.
A305713 counts pairwise coprime strict partitions.
A337561 counts pairwise coprime strict compositions.
A337665 counts compositions whose distinct parts are pairwise coprime, ranked by A333228.
A337697 counts pairwise coprime compositions with no 1's.
A337983 counts pairwise non-coprime strict compositions, with unordered version A318717 ranked by A318719.
Cf. A051424, A056239, A087087, A112798, A200976, A220377, A302569, A303140, A303282, A328673, A328867.
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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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