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A354235
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Heinz numbers of integer partitions with at least one part divisible by 3.
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2
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5, 10, 13, 15, 20, 23, 25, 26, 30, 35, 37, 39, 40, 45, 46, 47, 50, 52, 55, 60, 61, 65, 69, 70, 73, 74, 75, 78, 80, 85, 89, 90, 91, 92, 94, 95, 100, 103, 104, 105, 110, 111, 113, 115, 117, 120, 122, 125, 130, 135, 137, 138, 140, 141, 143, 145, 146, 148, 150
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OFFSET
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1,1
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COMMENTS
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The Heinz number of a 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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EXAMPLE
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The terms together with their prime indices begin:
5: {3}
10: {1,3}
13: {6}
15: {2,3}
20: {1,1,3}
23: {9}
25: {3,3}
26: {1,6}
30: {1,2,3}
35: {3,4}
37: {12}
39: {2,6}
40: {1,1,1,3}
45: {2,2,3}
46: {1,9}
47: {15}
50: {1,3,3}
52: {1,1,6}
55: {3,5}
60: {1,1,2,3}
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MATHEMATICA
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Select[Range[100], MemberQ[PrimePi/@First/@If[#==1, {}, FactorInteger[#]]/3, _?IntegerQ]&]
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CROSSREFS
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This sequence ranks the partitions counted by A295341, compositions A335464.
A046099 lists non-cubefree numbers.
A354234 counts partitions of n with at least one part divisible by k.
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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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