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A325179
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Heinz numbers of integer partitions such that the difference between the length of the minimal square containing and the maximal square contained in the Young diagram is 1.
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7
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3, 4, 6, 15, 18, 25, 27, 30, 45, 50, 75, 175, 245, 250, 343, 350, 375, 490, 525, 625, 686, 735, 875, 1029, 1225, 1715, 3773, 4802, 5929, 7203, 7546, 9317, 11319, 11858, 12005, 14641, 16807, 17787, 18634, 18865, 26411, 27951, 29282, 29645, 41503, 43923, 46585
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OFFSET
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1,1
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COMMENTS
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The enumeration of these partitions by sum is given by A325181.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
3: {2}
4: {1,1}
6: {1,2}
15: {2,3}
18: {1,2,2}
25: {3,3}
27: {2,2,2}
30: {1,2,3}
45: {2,2,3}
50: {1,3,3}
75: {2,3,3}
175: {3,3,4}
245: {3,4,4}
250: {1,3,3,3}
343: {4,4,4}
350: {1,3,3,4}
375: {2,3,3,3}
490: {1,3,4,4}
525: {2,3,3,4}
625: {3,3,3,3}
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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}]]]][[#]]>=#&]];
codurf[n_]:=If[n==1, 0, Max[PrimeOmega[n], PrimePi[FactorInteger[n][[-1, 1]]]]];
Select[Range[1000], codurf[#]-durf[#]==1&]
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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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