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A325233
Heinz numbers of integer partitions with Dyson rank 1.
15
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
OFFSET
1,1
COMMENTS
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).
EXAMPLE
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}
MATHEMATICA
Select[Range[1000], PrimePi[FactorInteger[#][[-1, 1]]]-PrimeOmega[#]==1&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 13 2019
STATUS
approved