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A307534
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Heinz numbers of strict integer partitions with 3 parts, all of which are odd.
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9
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110, 170, 230, 310, 374, 410, 470, 506, 590, 670, 682, 730, 782, 830, 902, 935, 970, 1030, 1034, 1054, 1090, 1265, 1270, 1298, 1370, 1394, 1426, 1474, 1490, 1570, 1598, 1606, 1670, 1705, 1790, 1826, 1886, 1910, 1955, 1970, 2006, 2110, 2134, 2162, 2255, 2266
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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 A001399.
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:
110: {1,3,5}
170: {1,3,7}
230: {1,3,9}
310: {1,3,11}
374: {1,5,7}
410: {1,3,13}
470: {1,3,15}
506: {1,5,9}
590: {1,3,17}
670: {1,3,19}
682: {1,5,11}
730: {1,3,21}
782: {1,7,9}
830: {1,3,23}
902: {1,5,13}
935: {3,5,7}
970: {1,3,25}
1030: {1,3,27}
1034: {1,5,15}
1054: {1,7,11}
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MATHEMATICA
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Select[Range[1000], SquareFreeQ[#]&&PrimeNu[#]==3&&OddQ[Times@@PrimePi/@First/@FactorInteger[#]]&]
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CROSSREFS
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Cf. A001221, A001222, A001399, A005117, A007304, A014612, A037144, A051037, A056239, A080193, A080257, A112798, A143207, A304636.
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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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