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A325235
Heinz numbers of integer partitions with Dyson rank 1 or -1.
3
3, 4, 10, 12, 15, 18, 25, 27, 28, 40, 42, 60, 63, 70, 88, 90, 98, 100, 105, 112, 132, 135, 147, 150, 168, 175, 198, 208, 220, 225, 245, 250, 252, 280, 297, 308, 312, 330, 343, 352, 375, 378, 392, 420, 462, 468, 484, 495, 520, 528, 544, 550, 567, 588, 625, 630
OFFSET
1,1
COMMENTS
Numbers whose maximum prime index and number of prime indices counted with multiplicity differ by 1.
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}
4: {1,1}
10: {1,3}
12: {1,1,2}
15: {2,3}
18: {1,2,2}
25: {3,3}
27: {2,2,2}
28: {1,1,4}
40: {1,1,1,3}
42: {1,2,4}
60: {1,1,2,3}
63: {2,2,4}
70: {1,3,4}
88: {1,1,1,5}
90: {1,2,2,3}
98: {1,4,4}
100: {1,1,3,3}
105: {2,3,4}
112: {1,1,1,1,4}
MATHEMATICA
Select[Range[1000], Abs[PrimePi[FactorInteger[#][[-1, 1]]]-PrimeOmega[#]]==1&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 13 2019
STATUS
approved