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A325164
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Heinz numbers of integer partitions with Durfee square of length 2.
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17
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9, 15, 18, 21, 25, 27, 30, 33, 35, 36, 39, 42, 45, 49, 50, 51, 54, 55, 57, 60, 63, 65, 66, 69, 70, 72, 75, 77, 78, 81, 84, 85, 87, 90, 91, 93, 95, 98, 99, 100, 102, 105, 108, 110, 111, 114, 115, 117, 119, 120, 121, 123, 126, 129, 130, 132, 133, 135, 138, 140
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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).
First differs from A105441 in lacking 125.
The Durfee length 1 case is A093641. The enumeration of Durfee length 2 partitions by sum is given by A006918, while that of Durfee length 3 partitions is given by A117485.
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
9: {2,2}
15: {2,3}
18: {1,2,2}
21: {2,4}
25: {3,3}
27: {2,2,2}
30: {1,2,3}
33: {2,5}
35: {3,4}
36: {1,1,2,2}
39: {2,6}
42: {1,2,4}
45: {2,2,3}
49: {4,4}
50: {1,3,3}
51: {2,7}
54: {1,2,2,2}
55: {3,5}
57: {2,8}
60: {1,1,2,3}
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MATHEMATICA
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durf[n_]:=Length[Select[Range[PrimeOmega[n]], Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]][[#]]>=#&]];
Select[Range[100], durf[#]==2&]
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CROSSREFS
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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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