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A325233
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Heinz numbers of integer partitions with Dyson rank 1.
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15
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3, 10, 15, 25, 28, 42, 63, 70, 88, 98, 105, 132, 147, 175, 198, 208, 220, 245, 297, 308, 312, 330, 343, 462, 468, 484, 495, 520, 544, 550, 693, 702, 726, 728, 770, 780, 816, 825, 1053, 1078, 1089, 1092, 1144, 1155, 1170, 1210, 1216, 1224, 1300, 1352, 1360
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OFFSET
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1,1
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COMMENTS
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Numbers whose maximum prime index is one greater than their number of prime indices counted with multiplicity.
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}
10: {1,3}
15: {2,3}
25: {3,3}
28: {1,1,4}
42: {1,2,4}
63: {2,2,4}
70: {1,3,4}
88: {1,1,1,5}
98: {1,4,4}
105: {2,3,4}
132: {1,1,2,5}
147: {2,4,4}
175: {3,3,4}
198: {1,2,2,5}
208: {1,1,1,1,6}
220: {1,1,3,5}
245: {3,4,4}
297: {2,2,2,5}
308: {1,1,4,5}
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MATHEMATICA
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Select[Range[1000], PrimePi[FactorInteger[#][[-1, 1]]]-PrimeOmega[#]==1&]
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CROSSREFS
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Cf. A001222, A047993, A056239, A061395, A063995, A101198, A106529, A112798, A257990, A263297, A325225, A325234, A325235.
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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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