A325761 Heinz numbers of integer partitions whose length is itself a part.

1, 2, 6, 9, 15, 20, 21, 30, 33, 39, 45, 50, 51, 56, 57, 69, 70, 75, 84, 87, 93, 105, 110, 111, 123, 125, 126, 129, 130, 140, 141, 159, 165, 170, 175, 176, 177, 183, 189, 190, 195, 196, 201, 210, 213, 219, 230, 237, 245, 249, 255, 264, 267, 275, 285, 290, 291

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).

The enumeration of these partitions by sum is given by A002865.

Examples

			The sequence of terms together with their prime indices begins:
    1: {}
    2: {1}
    6: {1,2}
    9: {2,2}
   15: {2,3}
   20: {1,1,3}
   21: {2,4}
   30: {1,2,3}
   33: {2,5}
   39: {2,6}
   45: {2,2,3}
   50: {1,3,3}
   51: {2,7}
   56: {1,1,1,4}
   57: {2,8}
   69: {2,9}
   70: {1,3,4}
   75: {2,3,3}
   84: {1,1,2,4}
   87: {2,10}
		

Crossrefs

Cf. A001222, A002865, A056239, A093641, A109298, A110295, A112798, A118914, A325762, A325763.

Programs

Mathematica

Select[Range[100],MemberQ[PrimePi/@First/@FactorInteger[#],PrimeOmega[#]]&]