A325235 Heinz numbers of integer partitions with Dyson rank 1 or -1.

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

Author

Gus Wiseman, Apr 13 2019

Keywords

• nonn

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).

Examples

			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}
		

Links

• FindStat, St000145: The Dyson rank of a partition

Crossrefs

Positions of 1's and -1's in A257541.

Cf. A001222, A047993, A056239, A061395, A063995, A101198, A106529, A112798, A257990, A263297, A325225, A325233, A325234.

Programs

Mathematica

Select[Range[1000],Abs[PrimePi[FactorInteger[#][[-1,1]]]-PrimeOmega[#]]==1&]