login
A325234
Heinz numbers of integer partitions with Dyson rank -1.
3
4, 12, 18, 27, 40, 60, 90, 100, 112, 135, 150, 168, 225, 250, 252, 280, 352, 375, 378, 392, 420, 528, 567, 588, 625, 630, 700, 792, 832, 880, 882, 945, 980, 1050, 1188, 1232, 1248, 1320, 1323, 1372, 1470, 1575, 1750, 1782, 1848, 1872, 1936, 1980, 2058, 2080
OFFSET
1,1
COMMENTS
Numbers whose maximum prime index is one fewer 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:
4: {1,1}
12: {1,1,2}
18: {1,2,2}
27: {2,2,2}
40: {1,1,1,3}
60: {1,1,2,3}
90: {1,2,2,3}
100: {1,1,3,3}
112: {1,1,1,1,4}
135: {2,2,2,3}
150: {1,2,3,3}
168: {1,1,1,2,4}
225: {2,2,3,3}
250: {1,3,3,3}
252: {1,1,2,2,4}
280: {1,1,1,3,4}
352: {1,1,1,1,1,5}
375: {2,3,3,3}
378: {1,2,2,2,4}
392: {1,1,1,4,4}
MATHEMATICA
Select[Range[1000], PrimePi[FactorInteger[#][[-1, 1]]]-PrimeOmega[#]==-1&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 13 2019
STATUS
approved