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A307373
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Heinz numbers of integer partitions with at least three parts, the third of which is 2.
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1
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27, 45, 54, 63, 75, 81, 90, 99, 105, 108, 117, 126, 135, 147, 150, 153, 162, 165, 171, 180, 189, 195, 198, 207, 210, 216, 225, 231, 234, 243, 252, 255, 261, 270, 273, 279, 285, 294, 297, 300, 306, 315, 324, 330, 333, 342, 345, 351, 357, 360, 363, 369, 378, 387
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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).
The enumeration of these partitions by sum is given by A006918 (see Emeric Deutsch's comment there).
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LINKS
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Table of n, a(n) for n=1..54.
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EXAMPLE
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The sequence of terms together with their prime indices begins:
27: {2,2,2}
45: {2,2,3}
54: {1,2,2,2}
63: {2,2,4}
75: {2,3,3}
81: {2,2,2,2}
90: {1,2,2,3}
99: {2,2,5}
105: {2,3,4}
108: {1,1,2,2,2}
117: {2,2,6}
126: {1,2,2,4}
135: {2,2,2,3}
147: {2,4,4}
150: {1,2,3,3}
153: {2,2,7}
162: {1,2,2,2,2}
165: {2,3,5}
171: {2,2,8}
180: {1,1,2,2,3}
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], PrimeOmega[#]>=3&&Reverse[primeMS[#]][[3]]==2&]
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CROSSREFS
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Cf. A000726, A002620, A004250, A006918, A056239, A097701, A112798, A257990, A297113, A325164, A325169, A325170.
Sequence in context: A253919 A357077 A259504 * A121614 A046340 A046316
Adjacent sequences: A307370 A307371 A307372 * A307374 A307375 A307376
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Apr 05 2019
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STATUS
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approved
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