A325706 Heinz numbers of integer partitions containing all of their distinct multiplicities.

1, 2, 6, 9, 10, 12, 14, 18, 22, 26, 30, 34, 36, 38, 40, 42, 46, 58, 60, 62, 66, 70, 74, 78, 82, 84, 86, 90, 94, 102, 106, 110, 112, 114, 118, 120, 122, 125, 126, 130, 132, 134, 138, 142, 146, 150, 154, 156, 158, 166, 170, 174, 178, 180, 182, 186, 190, 194, 198

Offset: 1

Author

Gus Wiseman, May 18 2019

Keywords

• nonn

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Also numbers n divisible by the squarefree kernel of their "shadow" A181819(n).

The enumeration of these partitions by sum is given by A325705.

Examples

			The sequence of terms together with their prime indices begins:
    1: {}
    2: {1}
    6: {1,2}
    9: {2,2}
   10: {1,3}
   12: {1,1,2}
   14: {1,4}
   18: {1,2,2}
   22: {1,5}
   26: {1,6}
   30: {1,2,3}
   34: {1,7}
   36: {1,1,2,2}
   38: {1,8}
   40: {1,1,1,3}
   42: {1,2,4}
   46: {1,9}
   58: {1,10}
   60: {1,1,2,3}
   62: {1,11}
		

Crossrefs

Cf. A056239, A109297, A112798, A114639, A114640, A181819, A225486, A290689, A324753, A324843, A325702, A325705, A325707, A325755.

Programs

Mathematica

Select[Range[100],#==1||SubsetQ[PrimePi/@First/@FactorInteger[#],Last/@FactorInteger[#]]&]