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A316430
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Heinz numbers of integer partitions whose length is equal to the GCD of all the parts.
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10
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1, 2, 9, 21, 39, 57, 87, 91, 111, 125, 129, 159, 183, 203, 213, 237, 247, 267, 301, 303, 321, 325, 339, 377, 393, 417, 427, 453, 489, 519, 543, 551, 553, 559, 575, 579, 597, 669, 687, 689, 707, 717, 753, 789, 791, 813, 817, 843, 845, 879, 923, 925, 933, 951, 973
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OFFSET
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1,2
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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).
2 is the only even term in the sequence. 3k is in the sequence if and only if k is in A031215. 5k is in the sequence if and only if k = pq with p and q in A031336.
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LINKS
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FORMULA
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EXAMPLE
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Sequence of integer partitions whose length is equal to their GCD begins: (), (1), (2,2), (4,2), (6,2), (8,2), (10,2), (6,4), (12,2), (3,3,3), (14,2), (16,2), (18,2), (10,4), (20,2), (22,2), (8,6), (24,2), (14,4), (26,2), (28,2), (6,3,3).
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MATHEMATICA
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Select[Range[200], PrimeOmega[#]==GCD@@Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]]&]
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PROG
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CROSSREFS
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Cf. A056239, A067538, A074761, A143773, A289508, A289509, A296150, A316413, A316431, A316432, A316433, A031215, A031336.
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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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